Finding Side Length (Given Perimeter) 2 worksheet - Free Printable

Let’s solve each problem one by one.
We’re given the perimeter of a rectangle and one side length, and we need to find the missing side labeled “L”.

Remember:
Perimeter of a rectangle = 2 × (length + width)
So if we know the perimeter and one side, we can rearrange the formula to find the other side.

Formula to find L:
If P = perimeter, and one side is known (let’s call it S), then:
P = 2 × (L + S) → divide both sides by 2 → P/2 = L + S → so L = P/2 - S

Let’s apply this to each problem:

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7) Perimeter = 12, one side = 2
L = 12 ÷ 2 - 2 = 6 - 2 = 4

8) Perimeter = 26, one side = 5
L = 26 ÷ 2 - 5 = 13 - 5 = 8

9) Perimeter = 22, one side = 5
L = 22 ÷ 2 - 5 = 11 - 5 = 6

10) Perimeter = 30, one side = 8
L = 30 ÷ 2 - 8 = 15 - 8 = 7

11) Perimeter = 24, one side = 7
L = 24 ÷ 2 - 7 = 12 - 7 = 5

12) Perimeter = 36, one side = 8
L = 36 ÷ 2 - 8 = 18 - 8 = 10

13) Perimeter = 20, one side = 8
L = 20 ÷ 2 - 8 = 10 - 8 = 2

14) Perimeter = 24, one side = 9
L = 24 ÷ 2 - 9 = 12 - 9 = 3

15) Perimeter = 32, one side = ? Wait — in the image, for #15, only “L” is shown on the right side, and no number is given for the bottom or top. But looking again — actually, in #15, the rectangle has “L” on the right side, and no number on any side? That can’t be right.

Wait — let me double-check the original image description.

Actually, in problem 15, the rectangle shows “L” on the right side, but no number on the bottom or top. However, since it’s a rectangle, opposite sides are equal. If only “L” is labeled, that means both vertical sides are L, and the horizontal sides must also be equal — but we don’t have their value.

But wait — perhaps I misread. Let me re-express:

Looking back at the user’s input:

For #15: “perimeter = 32”, and the diagram shows a square-like shape with “L” on the right side. But no number is given for the bottom side. Hmm.

Wait — maybe it’s implied that the bottom side is also L? No, because then it would be a square, and perimeter = 4L → 4L=32 → L=8. But that might not be correct unless specified.

Alternatively — perhaps there’s a typo in my reading. Let me check the original list again.

Actually, in the user’s message, for #15, it says:

“15) perimeter = 32
[diagram]
L”

And the diagram is drawn as a rectangle with “L” on the right side, and no number on the bottom. But in all other problems, one side is given numerically. So likely, for #15, the bottom side is also meant to be L? Or perhaps it's a square?

Wait — looking at the pattern: in problems 7–14, one side is given as a number, and L is the unknown. In #15, only L is labeled — which suggests that maybe both dimensions are L? i.e., it’s a square?

That makes sense — because if it’s a square, perimeter = 4 × side → 4L = 32 → L = 8.

Alternatively, if it’s a rectangle and only one side is labeled L, but no other number is given, then we can’t solve it — but that doesn’t make sense for a worksheet.

Given the context, and that all other problems give one numerical side, I think for #15, it’s intended to be a square — so all sides are L.

Thus:
Perimeter = 4 × L = 32 → L = 32 ÷ 4 = 8

Alternatively, if it were a rectangle with two sides L and two sides X, but X is not given, we couldn’t solve — so it must be a square.

I’ll go with L = 8 for #15.

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Now, let’s compile all answers:

7) 4
8) 8
9) 6
10) 7
11) 5
12) 10
13) 2
14) 3
15) 8

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