Question

question find the length of the third side. if necessary, write in simplest radical form. answer attempt 1 out of 3 8 2√41 submit answer watch video show examples

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), \(c^{2}=a^{2}+b^{2}\). Let \(a = 8\), \(c=2\sqrt{41}\), and we need to find \(b\). Then \((2\sqrt{41})^{2}=8^{2}+b^{2}\).

Step2: Expand the squares

\(4\times41=64 + b^{2}\), so \(164=64 + b^{2}\).

Step3: Solve for \(b^{2}\)

Subtract 64 from both sides: \(b^{2}=164 - 64\). Then \(b^{2}=100\).

Step4: Find \(b\)

Take the square root of both sides. Since \(b>0\) (length of a side), \(b = 10\).

Answer:

\(10\)