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, $a = 5$, $b = 12$, and $c=x$.
So, $x^{2}=5^{2}+12^{2}$.

Step2: Calculate the squares

$5^{2}=25$ and $12^{2}=144$. Then $x^{2}=25 + 144$.

Step3: Add the values

$x^{2}=169$.

Step4: 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. So, $x=\sqrt{169}=13$.

Answer:

13