Question

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

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

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

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

21, 16, & 12

Answer 1

What is the value of x
if 13, 84, x
is a Pythagorean triple?(1 point)
Responses

97
97

86
86

85
85

94

Answer 2

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

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

Let's go through each of the provided sets of side lengths:

1. **9, 12, & 14**
- Here, \( c = 14 \), \( a = 9 \), and \( b = 12 \).
- Check: \( 9^2 + 12^2 = 14^2 \)
- \( 81 + 144 = 196 \)
- \( 225 \neq 196 \) (not a right triangle)

2. **30, 24, & 18**
- Here, \( c = 30 \), \( a = 24 \), and \( b = 18 \).
- Check: \( 24^2 + 18^2 = 30^2 \)
- \( 576 + 324 = 900 \)
- \( 900 = 900 \) (is a right triangle)

3. **24, 7, & 26**
- Here, \( c = 26 \), \( a = 24 \), and \( b = 7 \).
- Check: \( 24^2 + 7^2 = 26^2 \)
- \( 576 + 49 = 676 \)
- \( 625 \neq 676 \) (not a right triangle)

4. **21, 16, & 12**
- Here, \( c = 21 \), \( a = 16 \), and \( b = 12 \).
- Check: \( 16^2 + 12^2 = 21^2 \)
- \( 256 + 144 = 441 \)
- \( 400 \neq 441 \) (not a right triangle)

Based on the tests above, the only set of side lengths that forms a right triangle is:

**30, 24, & 18**.