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, $a = 12$, $b = 35$, and $x$ is the hypotenuse. So, $x^{2}=12^{2}+35^{2}$.

Step2: Calculate squares

$12^{2}=144$ and $35^{2}=1225$. Then $x^{2}=144 + 1225$.

Step3: Sum the values

$x^{2}=1369$.

Step4: Find the square - root

$x=\sqrt{1369}=37$.

Answer:

37