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 and $a$ and $b$ are the legs. Here, $a = 9$, $b = 40$, and $c=x$. So, $x^{2}=9^{2}+40^{2}$.

Step2: Calculate squares

$9^{2}=81$ and $40^{2}=1600$. Then $x^{2}=81 + 1600$.

Step3: Sum the values

$x^{2}=1681$.

Step4: Find the square - root

$x=\sqrt{1681}=41$.

Answer:

41