Question

question find the length of the third side. if necessary, write in simplest radical form. answer attempt 1 out of 3

Explanation:

Step1: Apply the Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\). Let \(a = 10\), \(c=2\sqrt{41}\), and we need to find \(b\).
So, \(b^{2}=c^{2}-a^{2}\).

Step2: Substitute the values

Substitute \(a = 10\) and \(c = 2\sqrt{41}\) into the formula:
\(b^{2}=(2\sqrt{41})^{2}-10^{2}\).
First, \((2\sqrt{41})^{2}=4\times41 = 164\) and \(10^{2}=100\).
Then \(b^{2}=164 - 100=64\).

Step3: Solve for \(b\)

Take the square root of both sides: \(b=\sqrt{64}\).

Answer:

\(8\)