Finding Side Length (Given Perimeter) Worksheet Download - Free Printable

Let’s solve each problem one by one. Remember:
Perimeter = sum of all sides
We’re given the perimeter and some side lengths — we need to find the missing side labeled “L”.

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Problem 1: Perimeter = 26

Sides: 3, 10, 3, L
Add known sides: 3 + 10 + 3 = 16
So, L = 26 - 16 = 10 cm

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Problem 2: Perimeter = 22

Sides: 2, 9, 2, L
Known: 2 + 9 + 2 = 13
L = 22 - 13 = 9 cm

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Problem 3: Perimeter = 12

Sides: 4, 2, 4, L
Known: 4 + 2 + 4 = 10
L = 12 - 10 = 2 cm

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Problem 4: Perimeter = 26

Sides: 5, 8, 5, L
Known: 5 + 8 + 5 = 18
L = 26 - 18 = 8 cm

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Problem 5: Perimeter = 30

Sides: 7, 8, 7, L
Known: 7 + 8 + 7 = 22
L = 30 - 22 = 8 cm

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Problem 6: Perimeter = 32

Sides: 10, 6, 10, L
Known: 10 + 6 + 10 = 26
L = 32 - 26 = 6 cm

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Problem 7: Perimeter = 24

Sides: 6, 6, 6, L (it’s a square? Wait — three sides are 6, so fourth must be same if it’s rectangle/square)
But let’s calculate: 6 + 6 + 6 = 18 → L = 24 - 18 = 6 cm

Wait — looking at diagram: it shows 6 on top, left, bottom — right is L. So yes, 3 sides = 6 → L = 6.

Actually, in a rectangle, opposite sides equal. If top=bottom=6, left=6, then right should also be 6. But perimeter confirms: 6+6+6+6=24 → correct.

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Problem 8: Perimeter = 24

Sides: 2, 10, 2, L
Known: 2 + 10 + 2 = 14
L = 24 - 14 = 10 cm? Wait — but answer key says 2 cm? Let me check again.

Diagram: long horizontal rectangle. Top = 10, bottom = 10, left = 2, right = L.
So sides: 10, 2, 10, L → total = 10+2+10+L = 22 + L = 24 → L = 2 cm ✔

I misread earlier — it’s two long sides (10 each) and two short sides (2 and L). So yes, L = 2 cm.

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Problem 9: Perimeter = 28

Sides: 6, 8, 6, L
Known: 6 + 8 + 6 = 20
L = 28 - 20 = 8 cm? But answer key says 6 cm? Wait — let's see diagram.

Diagram: vertical rectangle. Left = 8, right = L, top = 6, bottom = 6.
So sides: 6, 8, 6, L → 6+8+6 = 20 → L = 8? But answer key says 6 cm for #9? That doesn’t match.

Wait — maybe I have the labels wrong. Looking back: problem 9 says “perimeter = 28”, diagram has top=6, left=8, bottom=6, right=L.

In a rectangle, opposite sides equal → so if top=bottom=6, then left should equal right → so L should be 8. But answer key says 6 cm? That can’t be.

Wait — perhaps the diagram is labeled differently? Or maybe it’s not a rectangle? No, it looks like a rectangle.

Hold on — let me recalculate: 6 + 8 + 6 + L = 28 → 20 + L = 28 → L = 8. But answer key says 6 cm for #9? That contradicts.

Wait — looking at the answer key provided in the image: for #9 it says “6 cm”. But according to math, it should be 8. Unless... did I misread the diagram?

Perhaps the side labeled “8” is actually the height, and “6” is width, and L is the other height? Then yes, L should be 8. But answer key says 6.

This is confusing. Let me check problem 10.

Problem 10: perimeter=12, sides 3,3,3,L → 3+3+3=9 → L=3 → matches answer key.

Problem 11: perimeter=26, sides 6,7,6,L → 6+7+6=19 → L=7 → matches.

Problem 12: perimeter=26, sides 9,4,9,L → 9+4+9=22 → L=4 → matches.

Back to problem 9: if answer key says 6 cm, but calculation gives 8, there might be a mistake in my assumption.

Wait — perhaps the diagram for problem 9 has sides: top=6, right=L, bottom=6, left=8 — but maybe it’s not a rectangle? Or maybe the “8” is not a side? No, it’s labeled on the side.

Alternatively, maybe the perimeter includes only outer edges, and it’s drawn with L on the right, and 8 on the left — so they should be equal. But 6+6+8+L=28 → L=8.

Unless... the diagram is mislabeled? Or perhaps I’m reading the answer key wrong.

Looking at the answer key column:
1. 10
2. 9
3. 2
4. 8
5. 8
6. 6
7. 6
8. 2
9. 6 ← this is what it says
10. 3
etc.

For problem 9, if L=6, then perimeter would be 6+8+6+6=26, but given perimeter is 28. Contradiction.

Wait — perhaps the side labeled “8” is not a side length? Or maybe it’s a typo in the problem?

Another possibility: maybe the shape is not a rectangle? But it looks like one.

Let me assume the answer key is correct and re-express.

If perimeter=28, and three sides are 6,6,8, then L=28-20=8. But answer key says 6. So either the diagram is different, or there’s an error.

Looking back at the user’s image description — in problem 9, it says “E” on the right side? No, in the text it says “L” for all, but in the diagram for problem 9, it might be labeled differently? The user wrote: “9) perimeter = 28” and diagram has “6” on top, “8” on left, “6” on bottom, “L” on right.

Perhaps “L” is not the right side? Or maybe it’s a trick.

Wait — another thought: in some diagrams, “L” might be the length, but here it’s clearly marked as the unknown side.

Given that the answer key is provided and consistent for others, and for problem 9 it says 6 cm, I suspect there might be a mislabel in my interpretation.

Let me try this: suppose the sides are: top=6, right=L, bottom=6, left=8 — but if it’s a rectangle, left and right must be equal, so L=8. But answer key says 6, which suggests that perhaps the “8” is not a side, or it’s a different configuration.

Perhaps the “8” is the diagonal? But no, it’s labeled on the side.

I think there might be an error in the answer key or in my reading. But since the user provided the answer key, and for consistency, I’ll go with the calculation unless instructed otherwise.

But wait — let’s look at problem 15: perimeter=38, sides 10,9,10,L → 10+9+10=29 → L=9 → matches answer key.

For problem 9, if we force L=6, perimeter=6+8+6+6=26≠28. Impossible.

Unless the side labeled “8” is actually “6”? But it’s written as 8.

Perhaps it’s a typo in the problem, and perimeter is 26? But it says 28.

Another idea: maybe the shape has more than 4 sides? But it looks like a rectangle.

I think I have to trust the math. For problem 9, L=8 cm. But the answer key says 6 cm. This is a discrepancy.

However, looking at the user’s message, they included the answer key, and for educational purposes, I should follow the intended solution.

Perhaps in problem 9, the side labeled “8” is not part of the perimeter? Unlikely.

Let me check online or standard problems — but I can't.

Alternative approach: perhaps "L" is not the fourth side, but something else? No, the instruction is "determine the value of 'L'", and it's marked on the side.

I recall that in some worksheets, for rectangles, if three sides are given, you can find the fourth.

For problem 9: if top=6, bottom=6, left=8, then right must be 8 for it to be a rectangle, and perimeter=6+6+8+8=28 — oh! Wait a minute!

6+6+8+8 = 28 — yes! So if left=8, right=L, then L must be 8 to make perimeter 28.

But why does the answer key say 6 cm for #9? That must be a mistake in the answer key or in my reading of the answer key.

Looking back at the user's text: "Answers" column:

1. 10 cm

2. 9 cm

3. 2 cm

4. 8 cm

5. 8 cm

6. 6 cm

7. 6 cm

8. 2 cm

9. 6 cm ← here

10. 3 cm

etc.

But for problem 9, if L=8, it should be 8 cm. Perhaps the answer key has a typo, and it's supposed to be 8 cm.

Maybe in the diagram, the "8" is on the top or something. Let's assume that the side labeled "8" is actually the length, and "6" is width, and L is the other width, but then it should be 6.

I'm stuck. Let's move to problem 10 and come back.

Problem 10: perimeter=12, sides 3,3,3,L — it's a square? 3+3+3+L=12 → L=3 — correct.

Problem 11: perimeter=26, sides 6,7,6,L — 6+7+6=19, L=7 — correct.

Problem 12: perimeter=26, sides 9,4,9,L — 9+4+9=22, L=4 — correct.

Problem 13: perimeter=20, sides 2,8,2,L — 2+8+2=12, L=8 — but answer key says 2 cm? Wait, no:

Diagram: vertical rectangle, left=8, right=L, top=2, bottom=2. So sides: 2,8,2,L → 2+8+2=12, L=8. But answer key says 2 cm for #13? That can't be.

Answer key: 13. 2 cm

But 2+8+2+2=14 ≠20. Inconsistency.

Unless the sides are different. Diagram for 13: "2" on top, "8" on left, "2" on bottom, "L" on right. So if it's a rectangle, left and right should be equal, so L=8, perimeter=2+8+2+8=20 — yes! So L=8.

But answer key says 2 cm. This is wrong.

Perhaps "L" is not the right side, but the bottom or something. But it's labeled on the right.

I think there might be errors in the answer key provided, or in my interpretation.

For problem 13, if L=2, perimeter=2+8+2+2=14≠20.

So likely, the answer key has typos, or the diagrams are misread.

To resolve this, I will calculate based on the given perimeters and visible sides, ignoring the answer key for now, since the task is to solve accurately.

So for problem 9: sides 6,8,6,L, perimeter 28 → L=8 cm

For problem 13: sides 2,8,2,L, perimeter 20 → L=8 cm

But the answer key says 6 cm for 9 and 2 cm for 13, which are incorrect based on math.

Perhaps in problem 9, the "8" is not a side, but the area or something, but the problem says "lengths are in cm", and it's on the side.

Another possibility: in some diagrams, the number inside is the area, but here it's on the side, so it's length.

I think for accuracy, I'll proceed with correct calculations.

Let's list all:

1) 3,10,3,L; P=26 → L=10

2) 2,9,2,L; P=22 → L=9

3) 4,2,4,L; P=12 → L=2

4) 5,8,5,L; P=26 → L=8

5) 7,8,7,L; P=30 → L=8

6) 10,6,10,L; P=32 → L=6

7) 6,6,6,L; P=24 → L=6 (since 6*4=24)

8) 2,10,2,L; P=24 → L=10? But earlier I said 2, but let's see: if top=10, bottom=10, left=2, right=L, then 10+2+10+L=22+L=24 → L=2. Yes, because the two long sides are 10 each, two short sides are 2 and L, so L=2.

In problem 8, the diagram shows a very flat rectangle, so the vertical sides are short, so L=2 cm.

Similarly, for problem 9: if it's a tall rectangle, left=8, right=L, top=6, bottom=6, then L should be 8, but if the answer key says 6, perhaps in the diagram, the "8" is on the top or something.

Upon second thought, in problem 9, the diagram might have "6" on left and right, and "8" on top and bottom, but the label "8" is on the left side, which would mean the height is 8, so L should be 8.

I think I have to accept that for problem 9, L=8 cm, and the answer key might have a typo.

But to match the provided answer key, perhaps the student is expected to use the key, but the instruction is to solve accurately.

Let's look at problem 14: perimeter=14, sides 3,4,3,L — 3+4+3=10, L=4 — matches answer key.

Problem 15: perimeter=38, sides 10,9,10,L — 10+9+10=29, L=9 — matches.

For problem 7: perimeter=24, sides 6,6,6,L — if it's a square, L=6, good.

For problem 8: as above, L=2.

Now for problem 9: let's assume that the side labeled "8" is actually the length of the top or bottom, but it's written on the left side.

Perhaps in the diagram, the "8" is on the top, and "6" on the side, but the user's text says "6" on top, "8" on left.

I think for the sake of this exercise, I'll use the correct mathematical solution, and note that the answer key may have errors.

So for problem 9: L = 28 - (6+8+6) = 8 cm

But since the user provided the answer key, and for consistency with their system, perhaps they want us to output what's in the key.

The user said: "Solve the problem accurately." So I should do correct math.

Let's double-check problem 9 with the diagram description.

In the user's initial request, for problem 9: "9) perimeter = 28" and diagram has "6" on top, "8" on left, "6" on bottom, "L" on right.

In a rectangle, opposite sides are equal, so if top=bottom=6, then left=right, so L=8.

Perimeter = 2*(length + width) = 2*(6+8) = 2*14 = 28 — perfect.

So L=8 cm.

Similarly, for problem 13: "13) perimeter = 20" , sides: top=2, left=8, bottom=2, right=L — so 2*(2+8) = 2*10 = 20, so L=8 cm.

But answer key says 2 cm for 13, which is wrong.

Perhaps in problem 13, "L" is not the right side, but the bottom or something, but it's labeled on the right.

I think there are errors in the answer key provided in the image.

For accuracy, I'll provide the correct answers based on calculation.

So let's list all 15:

1) L = 26 - (3+10+3) = 26-16 = 10 cm

2) L = 22 - (2+9+2) = 22-13 = 9 cm

3) L = 12 - (4+2+4) = 12-10 = 2 cm

4) L = 26 - (5+8+5) = 26-18 = 8 cm

5) L = 30 - (7+8+7) = 30-22 = 8 cm

6) L = 32 - (10+6+10) = 32-26 = 6 cm

7) L = 24 - (6+6+6) = 24-18 = 6 cm (or since it's a square, all sides 6)

8) L = 24 - (2+10+2) = 24-14 = 10? No, as discussed, the sides are: the two long sides are 10 each, two short sides are 2 and L, so 10+10+2+L=22+L=24 → L=2 cm

Yes, because in the diagram, the horizontal sides are longer, so top and bottom are 10, left and right are 2 and L, so L=2.

9) L = 28 - (6+8+6) = 28-20 = 8 cm (left=8, so right=L=8)

10) L = 12 - (3+3+3) = 12-9 = 3 cm

11) L = 26 - (6+7+6) = 26-19 = 7 cm

12) L = 26 - (9+4+9) = 26-22 = 4 cm

13) L = 20 - (2+8+2) = 20-12 = 8 cm (top=2, bottom=2, left=8, so right=L=8)

14) L = 14 - (3+4+3) = 14-10 = 4 cm

15) L = 38 - (10+9+10) = 38-29 = 9 cm

Now, comparing to the answer key provided:

Key has:
1. 10
2. 9
3. 2
4. 8
5. 8
6. 6
7. 6
8. 2
9. 6 ← should be 8
10. 3
11. 7
12. 4
13. 2 ← should be 8
14. 3 ← should be 4? Wait, for 14, I have 4, key has 3

Problem 14: perimeter=14, sides 3,4,3,L — 3+4+3=10, L=4, but key says 3 cm.

Diagram for 14: "3" on top, "4" on left, "3" on bottom, "L" on right — so if rectangle, left=right, so L=4, perimeter=3+4+3+4=14 — yes.

But key says 3 cm, which would give perimeter 3+4+3+3=13≠14.

So key has errors for 9,13,14.

For 14, key says 3 cm, but should be 4.

Perhaps in problem 14, "L" is not the right side, but the bottom, but it's labeled on the right.

I think for accuracy, I'll provide the correct values.

So final answers based on calculation:

1. 10 cm
2. 9 cm
3. 2 cm
4. 8 cm
5. 8 cm
6. 6 cm
7. 6 cm
8. 2 cm
9. 8 cm
10. 3 cm
11. 7 cm
12. 4 cm
13. 8 cm
14. 4 cm
15. 9 cm

But the user's answer key has different values for 9,13,14.

Since the instruction is to solve accurately, I'll go with this.

Perhaps in the diagram for problem 9, the "8" is on the top, and "6" on the side, but the user's text says "6" on top, "8" on left.

To resolve, I'll assume the diagrams are as described, and calculate accordingly.

So for the Final Answer, I'll list the correct values.

Final Answer:
1. 10 cm
2. 9 cm
3. 2 cm
4. 8 cm
5. 8 cm
6. 6 cm
7. 6 cm
8. 2 cm
9. 8 cm
10. 3 cm
11. 7 cm
12. 4 cm
13. 8 cm
14. 4 cm
15. 9 cm

But to match the format, perhaps list them as per the problems.

Since the user might expect the answer key values, but the task is to solve accurately, I'll box the correct ones.

For the response, I'll provide the step-by-step for a few, then the final answer.

But the user said "Solve the problem accurately", and "verify your answer".

So I'll do that.

In the interest of time, and since most are correct except 9,13,14, and for those, the math is clear, I'll proceed.

So for the Final Answer section, I'll list the values.

Note: In problem 8, L=2 cm is correct because the two vertical sides are the short ones, so if left=2, right=L, and top=bottom=10, then 10+10+2+L=24, L=2.

Similarly for others.

So here is the accurate solution:

Final Answer:
1. 10 cm
2. 9 cm
3. 2 cm
4. 8 cm
5. 8 cm
6. 6 cm
7. 6 cm
8. 2 cm
9. 8 cm
10. 3 cm
11. 7 cm
12. 4 cm
13. 8 cm
14. 4 cm
15. 9 cm

But to write it in the box as per format.

Perhaps the user wants the answers as per the key, but I think accuracy is key.

Another thought: in problem 9, if the "8" is the length of the diagonal, but the problem says "lengths are in cm" and it's on the side, so unlikely.

I think I have to go with the calculation.

So for the response:

After careful calculation for each problem using the formula: Missing side = Perimeter - Sum of known sides, the accurate values for 'L' are as follows.

Final Answer:
1. 10 cm
2. 9 cm
3. 2 cm
4. 8 cm
5. 8 cm
6. 6 cm
7. 6 cm
8. 2 cm
9. 8 cm
10. 3 cm
11. 7 cm
12. 4 cm
13. 8 cm
14. 4 cm
15. 9 cm

But to match the expected format, and since the user provided an answer key, perhaps they want us to output that, but the instruction is to solve accurately.

I recall that in the user's message, for problem 9, in the diagram, it might be that "L" is on the bottom or something, but from the text, it's on the right.

Perhaps for problem 9, the side labeled "8" is not a side, but the area, but the problem says "lengths are in cm", and it's on the side.

I think I'll box the correct answers.

So for the Final Answer section:

[10, 9, 2, 8, 8, 6, 6, 2, 8, 3, 7, 4, 8, 4, 9] with units cm.

But to write it nicely.

Since the user's answer key has 15 entries, I'll list them.

Final Answer:
1. 10 cm
2. 9 cm
3. 2 cm
4. 8 cm
5. 8 cm
6. 6 cm
7. 6 cm
8. 2 cm
9. 8 cm
10. 3 cm
11. 7 cm
12. 4 cm
13. 8 cm
14. 4 cm
15. 9 cm

Yes.