Question

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

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

24, 7, & 26
24, 7, & 26

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

30, 24, & 18

Answer 1

To determine which side lengths can form a right triangle, we can apply the Pythagorean theorem. According to the theorem, in a right triangle with sides \(a\), \(b\), and hypotenuse \(c\) (where \(c\) is the longest side), the following relationship must hold:

\[ a^2 + b^2 = c^2. \]

Let's analyze each set of lengths:

1. **21, 16, 12**
- Longest side \(c = 21\).
- Check: \(12^2 + 16^2 = 144 + 256 = 400\)
- Compare with \(21^2 = 441\)
- \(400 \neq 441\) (not a right triangle).

2. **24, 7, 26**
- Longest side \(c = 26\).
- Check: \(7^2 + 24^2 = 49 + 576 = 625\)
- Compare with \(26^2 = 676\)
- \(625 \neq 676\) (not a right triangle).

3. **9, 12, 14**
- Longest side \(c = 14\).
- Check: \(9^2 + 12^2 = 81 + 144 = 225\)
- Compare with \(14^2 = 196\)
- \(225 \neq 196\) (not a right triangle).

4. **30, 24, 18**
- Longest side \(c = 30\).
- Check: \(24^2 + 18^2 = 576 + 324 = 900\)
- Compare with \(30^2 = 900\)
- \(900 = 900\) (this is a right triangle).

Therefore, **the side lengths that would form a right triangle are 30, 24, and 18**.