Question

for the following right triangle, find the side length x.

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse. Here, $a = 7$, $b = 24$, and $x$ is the hypotenuse. So $x^{2}=7^{2}+24^{2}$.

Step2: Calculate the squares

$7^{2}=49$ and $24^{2}=576$. Then $x^{2}=49 + 576$.

Step3: Add the values

$49+576 = 625$. So $x^{2}=625$.

Step4: Find the square - root

$x=\sqrt{625}=25$.

Answer:

$25$