Question

question 1 5 pts

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse and $a,b$ are the legs. Here, $c = 10$, $a=x$, $b = 6$. So, $x^{2}+6^{2}=10^{2}$.

Step2: Simplify the equation

$x^{2}+36 = 100$. Then, $x^{2}=100 - 36$.

Step3: Calculate the value of $x^{2}$

$x^{2}=64$.

Step4: Solve for $x$

Taking the square root of both sides, since $x$ represents a side - length and must be non - negative, $x=\sqrt{64}=8$.

Answer:

8