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, $a = 12$, $b = 16$, and $x$ is the hypotenuse. So $x^{2}=12^{2}+16^{2}$.

Step2: Calculate squares

$12^{2}=144$ and $16^{2}=256$. Then $x^{2}=144 + 256$.

Step3: Add values

$144+256 = 400$, so $x^{2}=400$.

Step4: Find square - root

$x=\sqrt{400}=20$.

Answer:

20