Question

in a right triangle, if a = 7 and c = 25, what is b?
a. 20
b. 24
c. 18
d. 23

in the pythagorean theorem a² + b² = c², what does c represent?
a. the base
b. the hypotenuse
c. one of the legs
d. the perimeter

Explanation:

Step1: Recall Pythagorean theorem

In a right - triangle, $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse and $a$ and $b$ are the legs. Given $a = 7$ and $c = 25$, we can solve for $b$ as $b=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

$b=\sqrt{25^{2}-7^{2}}=\sqrt{(25 + 7)(25 - 7)}=\sqrt{32\times18}=\sqrt{576}=24$.
For the second question, by the definition of the Pythagorean theorem, $c$ represents the hypotenuse of the right - triangle.

Answer:

1. b. 24
2. b. The hypotenuse