Question

solve for x. leave your answer in simplest radical form.

Explanation:

Step1: Find the length of the common side

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) for the right - triangle with sides \(7\) and \(10\). Let the common side be \(h\).
\(h^{2}=10^{2}-7^{2}\)
\(h^{2}=100 - 49\)
\(h^{2}=51\)

Step2: Solve for \(x\)

Use the Pythagorean theorem for the right - triangle with base \(8\) and height \(h\).
\(x^{2}=h^{2}+8^{2}\)
Since \(h^{2}=51\), then \(x^{2}=51 + 64\)
\(x^{2}=115\)
Take the square root of both sides: \(x=\sqrt{115}\)

Answer:

\(x = \sqrt{115}\)