Question

for the following right triangle, find the side length x. round your answer to the nearest hundredth.

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse. Here, $x$ is the hypotenuse, and the two legs are 8 and 10. So $x^{2}=8^{2}+10^{2}$.

Step2: Calculate the squares

$8^{2}=64$ and $10^{2}=100$. Then $x^{2}=64 + 100=164$.

Step3: Solve for $x$

$x=\sqrt{164}$. Simplify $\sqrt{164}=\sqrt{4\times41}=2\sqrt{41}\approx 12.81$.

Answer:

$12.81$