Question

Question was provided via image upload.

Explanation:

Step1: Identify the theorem

Use the Pythagorean theorem for right - triangles ($a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse).

Step2: Substitute values

Here, $a = 6$, $b = 8$, and $c=x$. So, $6^{2}+8^{2}=x^{2}$.

Step3: Calculate squares

$6^{2}=36$ and $8^{2}=64$. Then $36 + 64=x^{2}$, so $x^{2}=100$.

Step4: Solve for $x$

Take the square root of both sides. Since $x$ represents the length of a side, we take the positive square root. $x=\sqrt{100}=10$.

Answer:

$10$