Question

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

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. Here, $a = 9$, $b = 12$, and $c=x$.

Step2: Substitute values into the formula

$x^{2}=9^{2}+12^{2}$.
$x^{2}=81 + 144$.
$x^{2}=225$.

Step3: Solve for $x$

Take the square root of both sides. Since $x$ represents the length of a side of a triangle, we take the positive square root. $x=\sqrt{225}=15$.

Answer:

15