Question

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

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\). Let \(a = 2\sqrt{7}\), \(b\) be the unknown side, and \(c = 6\). Then \(b^{2}=c^{2}-a^{2}\).

Step2: Substitute values

\(b^{2}=6^{2}-(2\sqrt{7})^{2}\).
First, calculate \(6^{2}=36\) and \((2\sqrt{7})^{2}=4\times7 = 28\).
So \(b^{2}=36 - 28\).

Step3: Simplify

\(b^{2}=8\).
Since \(b>0\) (length of a side), \(b=\sqrt{8}\).
Simplify \(\sqrt{8}=\sqrt{4\times2}=2\sqrt{2}\).

Answer:

\(2\sqrt{2}\)