Question

find the length of the third side. if necessary, write in simplest radical form. answer attempt 1 out of 2

Explanation:

Step1: Apply Pythagorean theorem

Let the hypotenuse be $c = 2\sqrt{41}$ and one - leg be $a = 8$. The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, where $b$ is the unknown side. So, $b^{2}=c^{2}-a^{2}$.

Step2: Substitute the values

Substitute $c = 2\sqrt{41}$ and $a = 8$ into the formula. First, $c^{2}=(2\sqrt{41})^{2}=4\times41 = 164$ and $a^{2}=8^{2}=64$. Then $b^{2}=164 - 64$.

Step3: Calculate $b^{2}$

$b^{2}=164−64 = 100$.

Step4: Find $b$

Take the square - root of both sides. Since $b>0$ (as it represents the length of a side of a triangle), $b=\sqrt{100}=10$.

Answer:

$10$