Question

find the length of the third side. if necessary, write in simplest radical form

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a = 2\) and \(b=2\sqrt{3}\), and hypotenuse \(c\), the Pythagorean theorem is \(c=\sqrt{a^{2}+b^{2}}\).
Substitute \(a = 2\) and \(b = 2\sqrt{3}\) into the formula: \(c=\sqrt{2^{2}+(2\sqrt{3})^{2}}\).

Step2: Simplify the expression inside the square root

First, calculate \(2^{2}=4\) and \((2\sqrt{3})^{2}=4\times3 = 12\).
Then \(a^{2}+b^{2}=4 + 12=16\).

Step3: Calculate the square root

\(c=\sqrt{16}=4\).

Answer:

\(4\)