Area and Perimeter of Triangles - K12 Math Worksheets - Free Printable

Let's solve each problem step by step to find the perimeter of each right triangle. The perimeter of a triangle is the sum of the lengths of all three sides.

We'll go through each triangle one by one.

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1) Triangle with sides: 9 ft, 21 ft, and 23 ft

All three sides are given:
- 9 ft
- 21 ft
- 23 ft

Perimeter = 9 + 21 + 23 = 53 ft

✔ Check: Is this a right triangle?
Check using Pythagorean theorem:
$ 9^2 + 21^2 = 81 + 441 = 522 $
$ 23^2 = 529 $ → Not equal → Not a perfect right triangle (but the problem assumes it is).
But since the problem says "right triangle" and gives all three sides, we’ll assume the values are correct and just compute perimeter.

> Answer: 53 ft

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2) Triangle with sides: 9 yd, 5 yd, and 11 yd

Sides:
- 9 yd
- 5 yd
- 11 yd

Perimeter = 9 + 5 + 11 = 25 yd

Check if it’s a right triangle:
$ 5^2 + 9^2 = 25 + 81 = 106 $
$ 11^2 = 121 $ → Not equal → Not a right triangle?
Wait — but again, the problem labels it as a right triangle. Let's double-check side assignments.

Assuming the hypotenuse is the longest side (11 yd), then:

Is $ 5^2 + 9^2 = 11^2 $?
→ $ 25 + 81 = 106 $, $ 121 $ → No. So not a right triangle?

But let’s suppose the triangle is labeled correctly — maybe the hypotenuse is not 11 yd?

Wait: If 9 yd and 5 yd are legs, then hypotenuse should be:

$ \sqrt{9^2 + 5^2} = \sqrt{81 + 25} = \sqrt{106} \approx 10.3 $ yd — not 11.

So something's off.

But since the problem states it’s a right triangle and gives all three sides, perhaps we just accept the values and compute perimeter regardless.

> Perimeter = 9 + 5 + 11 = 25 yd

But let's check if any combination works:

Try: $ 5^2 + 11^2 = 25 + 121 = 146 $ → $ \sqrt{146} \approx 12.08 $

Try: $ 9^2 + 11^2 = 81 + 121 = 202 $ → $ \sqrt{202} \approx 14.2 $

No combination gives integer result. So likely this is not a right triangle, or there's a typo.

But since the worksheet says “Right Triangles”, and gives all three sides, we proceed with perimeter.

> Answer: 25 yd

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3) Triangle with sides: 7 cm, 6 cm, 9 cm

Given:
- 7 cm
- 6 cm
- 9 cm

Perimeter = 7 + 6 + 9 = 22 cm

Check if right triangle:
$ 6^2 + 7^2 = 36 + 49 = 85 $
$ 9^2 = 81 $ → Not equal → Not a right triangle.

Hmm — again, discrepancy.

But maybe the 9 cm is the hypotenuse?

Then $ 6^2 + 7^2 = 85 $, $ 9^2 = 81 $ → no.

Wait: $ 6^2 + 9^2 = 36 + 81 = 117 $, $ 7^2 = 49 $ → no.

Not a right triangle.

But perhaps the diagram shows legs as 6 and 7, hypotenuse as 9? But that doesn’t satisfy Pythagoras.

Wait: $ \sqrt{6^2 + 7^2} = \sqrt{85} \approx 9.22 $, so hypotenuse should be ~9.22, not 9.

So again, possibly a typo.

But we'll just add the sides.

> Answer: 22 cm

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4) Triangle with sides: 15 cm, 12 cm, 9 cm

Given:
- 15 cm (hypotenuse)
- 12 cm
- 9 cm

Check: $ 9^2 + 12^2 = 81 + 144 = 225 $
$ 15^2 = 225 $ → ✔ Yes! This is a right triangle.

Perimeter = 9 + 12 + 15 = 36 cm

> Answer: 36 cm

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5) Triangle with sides: 11 in, 12 in, 16 in

Sides:
- 11 in
- 12 in
- 16 in

Perimeter = 11 + 12 + 16 = 39 in

Check if right triangle:
$ 11^2 + 12^2 = 121 + 144 = 265 $
$ 16^2 = 256 $ → Not equal → Not a right triangle.

But again, assuming it's labeled as such, we just compute perimeter.

> Answer: 39 in

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6) Triangle with sides: 8 ft, 15 ft, 17 ft

Sides:
- 8 ft
- 15 ft
- 17 ft

Check: $ 8^2 + 15^2 = 64 + 225 = 289 $
$ 17^2 = 289 $ → ✔ Yes! Right triangle.

Perimeter = 8 + 15 + 17 = 40 ft

> Answer: 40 ft

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✔ Final Answers:

1) 53 ft
2) 25 yd
3) 22 cm
4) 36 cm
5) 39 in
6) 40 ft

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🔍 Summary of Key Points:

- Perimeter = sum of all three sides.
- For right triangles, the Pythagorean Theorem ($ a^2 + b^2 = c^2 $) holds for the two legs and hypotenuse.
- In problems 1, 2, 3, and 5, the side lengths do not satisfy the Pythagorean Theorem, suggesting possible errors in labeling or rounding.
- But since the problem asks for perimeter, and all sides are provided, we can still compute it directly.

> Only problems 4 and 6 are valid right triangles with exact integer side ratios (3-4-5 and 8-15-17 multiples).

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✔ Final Answer List:

| Problem | Perimeter |
|--------|-----------|
| 1) | 53 ft |
| 2) | 25 yd |
| 3) | 22 cm |
| 4) | 36 cm |
| 5) | 39 in |
| 6) | 40 ft |

Let me know if you'd like a version with explanations for students!