Question

18 of 2018 of 20 Items
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Question
Which side lengths represent the sides of a right triangle?
Responses
A 2, 3, 52, 3, 5
B 7, 24, 257, 24, 25
C 7, 23, 257, 23, 25
D 12, 16, 2112, 16, 21
E 12, 13, 17

Answer 1

To determine which side lengths represent the sides of a right triangle, we can use the Pythagorean theorem, which states that for a right triangle with side lengths \( a \), \( b \), and hypotenuse \( c \), the equation \( a^2 + b^2 = c^2 \) holds true.

Let's evaluate each option:

**A. 2, 3, 5**
- Check if \( 2^2 + 3^2 = 5^2 \):
\[
2^2 + 3^2 = 4 + 9 = 13 \quad \text{and} \quad 5^2 = 25 \quad \text{(Not a right triangle)}
\]

**B. 7, 24, 25**
- Check if \( 7^2 + 24^2 = 25^2 \):
\[
7^2 + 24^2 = 49 + 576 = 625 \quad \text{and} \quad 25^2 = 625 \quad \text{(Right triangle)}
\]

**C. 7, 23, 25**
- Check if \( 7^2 + 23^2 = 25^2 \):
\[
7^2 + 23^2 = 49 + 529 = 578 \quad \text{and} \quad 25^2 = 625 \quad \text{(Not a right triangle)}
\]

**D. 12, 16, 21**
- Check if \( 12^2 + 16^2 = 21^2 \):
\[
12^2 + 16^2 = 144 + 256 = 400 \quad \text{and} \quad 21^2 = 441 \quad \text{(Not a right triangle)}
\]

**E. 12, 13, 17**
- Check if \( 12^2 + 13^2 = 17^2 \):
\[
12^2 + 13^2 = 144 + 169 = 313 \quad \text{and} \quad 17^2 = 289 \quad \text{(Not a right triangle)}
\]

Based on the evaluations:
- **Only option B (7, 24, 25)** represents the sides of a right triangle.