Question

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

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

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

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

9, 12, & 14

Answer 1

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

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

Let's check each set of side lengths:

1. **21, 16, & 12**
- Longest side: 21
- Calculation: \( 16^2 + 12^2 = 256 + 144 = 400 \)
- \( 21^2 = 441 \)
- Not a right triangle.

2. **24, 7, & 26**
- Longest side: 26
- Calculation: \( 24^2 + 7^2 = 576 + 49 = 625 \)
- \( 26^2 = 676 \)
- Not a right triangle.

3. **30, 24, & 18**
- Longest side: 30
- Calculation: \( 24^2 + 18^2 = 576 + 324 = 900 \)
- \( 30^2 = 900 \)
- This is a right triangle!

4. **9, 12, & 14**
- Longest side: 14
- Calculation: \( 9^2 + 12^2 = 81 + 144 = 225 \)
- \( 14^2 = 196 \)
- Not a right triangle.

The side lengths that can form a right triangle are **30, 24, & 18**.