Question

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

Explanation:

Step1: Apply Pythagorean theorem

Let the length of the common - side of the two right - triangles be \(y\). In the upper right - triangle, by the Pythagorean theorem \(y^{2}=5^{2}-3^{2}\).
\[y^{2}=25 - 9=16\]
\[y = 4\]

Step2: Apply Pythagorean theorem again

In the lower right - triangle, using the Pythagorean theorem \(x^{2}+y^{2}=8^{2}\). Since \(y = 4\), we have \(x^{2}+16 = 64\).
\[x^{2}=64 - 16=48\]
\[x=\sqrt{48}=4\sqrt{3}\]

Answer:

\(4\sqrt{3}\)