Question

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

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

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

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

24, 7, & 26

Answer 1

To determine which sets of side lengths can form a right triangle, we can use the Pythagorean theorem, which states that for a right triangle with sides \(a\), \(b\), and \(c\) (where \(c\) is the longest side), the following equation must hold:

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

Let's check each of the provided sets of side lengths:

1. **9, 12, & 14**
- \(14^2 = 196\)
- \(9^2 + 12^2 = 81 + 144 = 225\)
- \(196 \neq 225\) → does not form a right triangle.

2. **21, 16, & 12**
- \(21^2 = 441\)
- \(16^2 + 12^2 = 256 + 144 = 400\)
- \(441 \neq 400\) → does not form a right triangle.

3. **30, 24, & 18**
- \(30^2 = 900\)
- \(24^2 + 18^2 = 576 + 324 = 900\)
- \(900 = 900\) → does form a right triangle.

4. **24, 7, & 26**
- \(26^2 = 676\)
- \(24^2 + 7^2 = 576 + 49 = 625\)
- \(676 \neq 625\) → does not form a right triangle.

Based on the checks, the only set of side lengths that can form a right triangle is:

**30, 24, & 18**.