Question

Which side lengths would form a right triangle?(1 point)
Responses

21, 16, & 12
21, 16, & 12

9, 12, & 14
9, 12, & 14

30, 24, & 18
30, 24, & 18

24, 7, & 26

Answer 1

To determine whether three given side lengths can form a right triangle, we can apply 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.

We'll evaluate each set of side lengths:

1. **21, 16, & 12**:
- Hypotenuse \(c = 21\)
- Check: \(16^2 + 12^2 = 256 + 144 = 400\)
- \(21^2 = 441\)
- Not a right triangle since \(400 \neq 441\).

2. **9, 12, & 14**:
- Hypotenuse \(c = 14\)
- Check: \(9^2 + 12^2 = 81 + 144 = 225\)
- \(14^2 = 196\)
- Not a right triangle since \(225 \neq 196\).

3. **30, 24, & 18**:
- Hypotenuse \(c = 30\)
- Check: \(24^2 + 18^2 = 576 + 324 = 900\)
- \(30^2 = 900\)
- This IS a right triangle since \(900 = 900\).

4. **24, 7, & 26**:
- Hypotenuse \(c = 26\)
- Check: \(24^2 + 7^2 = 576 + 49 = 625\)
- \(26^2 = 676\)
- Not a right triangle since \(625 \neq 676\).

Concluding, the sides that can form a right triangle are **30, 24, & 18**.