Question

find the length of the third side. if necessary, write in simplest radical form.
$2\sqrt{41}$
8
answer attempt 1 out of 2

Explanation:

Step1: Recall Pythagorean theorem

For right triangle: $a^2 + b^2 = c^2$, where $c$ is hypotenuse, $a=8$, $c=2\sqrt{41}$, solve for $b$.

Step2: Rearrange formula to solve for $b$

$b^2 = c^2 - a^2$

Step3: Substitute values into formula

$b^2 = (2\sqrt{41})^2 - 8^2 = 4\times41 - 64 = 164 - 64$

Step4: Calculate and simplify $b$

$b^2 = 100$, so $b = \sqrt{100} = 10$

Answer:

10