Worksheet for calculating missing side lengths of triangles using perimeter information.

It looks like you've uploaded a worksheet titled "Missing Side" that includes several geometry problems involving finding missing side lengths of triangles, given the perimeter and other side lengths. Let's go through each problem step by step.

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Problem 1: Find the missing side

We are given various triangles with two or more sides labeled and the perimeter provided. The goal is to find the missing side using:

> Perimeter = sum of all sides

So:
> Missing side = Perimeter − (sum of known sides)

Let’s solve each one.

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#### 1. Triangle with sides: 8, 6, ?
- Perimeter = 23 ft
- Known sides: 8 ft, 6 ft
- Missing side = 23 − (8 + 6) = 23 − 14 = 9 ft

✔ Answer: 9 ft

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#### 2. Triangle with sides: 10, ?, 15
- Perimeter = 37 in
- Known sides: 10 in, 15 in
- Missing side = 37 − (10 + 15) = 37 − 25 = 12 in

✔ Answer: 12 in

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#### 3. Triangle with sides: ?, 12 yd, 12 yd
- Perimeter = 36 yd
- Known sides: 12 yd, 12 yd
- Missing side = 36 − (12 + 12) = 36 − 24 = 12 yd

✔ Answer: 12 yd
*(This is an equilateral triangle!)*

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#### 4. Triangle with sides: 14 cm, 10 cm, ?
- Perimeter = 37 cm
- Known sides: 14 cm, 10 cm
- Missing side = 37 − (14 + 10) = 37 − 24 = 13 cm

✔ Answer: 13 cm

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#### 5. Triangle with sides: 12 m, 12 m, ?
- Perimeter = 40 m
- Known sides: 12 m, 12 m
- Missing side = 40 − (12 + 12) = 40 − 24 = 16 m

✔ Answer: 16 m

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#### 6. Triangle with sides: 14 ft, ?, 15 ft
- Perimeter = 16 ft
- Wait — this can't be right!

Let’s check:
- Two sides: 14 ft and 15 ft → already sum to 29 ft
- But the perimeter is only 16 ft, which is less than the sum of just two sides!

✘ This is impossible for a triangle.

Triangle Inequality Theorem: The sum of any two sides must be greater than the third side.

But here, even the sum of two sides (14 + 15 = 29) is greater than the perimeter (16), so it’s impossible.

So either:
- There’s a typo in the problem.
- Or the side labels are incorrect.

But assuming the perimeter is 16 ft, and one side is 14 ft, another is 15 ft, then:
- Total of known sides: 14 + 15 = 29 ft > 16 ft → Impossible.

So no such triangle exists.

But let’s suppose the perimeter is 46 ft instead of 16 ft? That would make sense.

Wait — maybe it's a typo in your image?

Looking at the image, it says:
> "Perimeter = 16 ft"

But with sides 14 ft and 15 ft, that’s impossible.

So unless one of the sides is mislabeled, this triangle cannot exist.

Let’s assume it’s a mistake and move on.

Alternatively, if the perimeter is 46 ft, then:
- Missing side = 46 − (14 + 15) = 46 − 29 = 17 ft

But since it says 16 ft, we must conclude:

🚫 No valid triangle exists with sides 14 ft, 15 ft, and perimeter 16 ft.

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Problem 7:

> The perimeter of a triangle is 38 cm. If the lengths of two sides are 14 cm and 17 cm, find the length of the third side.

Use:
- Third side = Perimeter − (14 + 17) = 38 − 31 = 7 cm

✔ Answer: 7 cm

Check triangle inequality:
- 14 + 17 > 7 → 31 > 7 ✔
- 14 + 7 > 17 → 21 > 17 ✔
- 17 + 7 > 14 → 24 > 14 ✔

So yes, valid triangle.

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Problem 8:

> If the perimeter of an equilateral triangle is 24 feet, determine the length of each side.

In an equilateral triangle, all three sides are equal.

Let each side = x

Then:
- Perimeter = 3x = 24
- x = 24 ÷ 3 = 8 feet

✔ Answer: 8 feet

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✔ Final Answers:

| Problem | Answer |
|--------|--------|
| 1 | 9 ft |
| 2 | 12 in |
| 3 | 12 yd |
| 4 | 13 cm |
| 5 | 16 m |
| 6 | ✘ Impossible (check for typo) |
| 7 | 7 cm |
| 8 | 8 ft |

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🛠️ Notes:

- For Problem 6, double-check the values. Likely a typo — perhaps the perimeter is 46 ft, not 16 ft.
- Otherwise, no triangle can have two sides totaling 29 ft and a perimeter of only 16 ft.

Let me know if you'd like help correcting or re-solving #6 with corrected data!