Question

Determine if a right triangle can be formed from the given measurements? Select all that apply.


8in, 15in, 17in


12in, 16in, 20in


5in, 12in, 13in


7in, 24in, 25in


11in, 18in, 21in


15in, 19in, 24in

Answer 1

To determine if a triangle is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle with legs \( a \) and \( b \), and hypotenuse \( c \), the relationship \( a^2 + b^2 = c^2 \) holds true.

We will test each set of measurements:

1. **8 in, 15 in, 17 in:**
- \( 17^2 = 289 \)
- \( 8^2 + 15^2 = 64 + 225 = 289 \)
- This is a right triangle.

2. **12 in, 16 in, 20 in:**
- \( 20^2 = 400 \)
- \( 12^2 + 16^2 = 144 + 256 = 400 \)
- This is a right triangle.

3. **5 in, 12 in, 13 in:**
- \( 13^2 = 169 \)
- \( 5^2 + 12^2 = 25 + 144 = 169 \)
- This is a right triangle.

4. **7 in, 24 in, 25 in:**
- \( 25^2 = 625 \)
- \( 7^2 + 24^2 = 49 + 576 = 625 \)
- This is a right triangle.

5. **11 in, 18 in, 21 in:**
- \( 21^2 = 441 \)
- \( 11^2 + 18^2 = 121 + 324 = 445 \)
- This is NOT a right triangle.

6. **15 in, 19 in, 24 in:**
- \( 24^2 = 576 \)
- \( 15^2 + 19^2 = 225 + 361 = 586 \)
- This is NOT a right triangle.

**Result:**
The following sets of measurements can form right triangles:
- **8 in, 15 in, 17 in**
- **12 in, 16 in, 20 in**
- **5 in, 12 in, 13 in**
- **7 in, 24 in, 25 in**