Question

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

Explanation:

Step1: Apply Pythagorean theorem

Let the third side be \(x\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 2\sqrt{5}\) (hypotenuse) and \(a = 2\) (one - leg). So, \(2^{2}+x^{2}=(2\sqrt{5})^{2}\).

Step2: Simplify the equation

\(4+x^{2}=4\times5\). Then \(4+x^{2}=20\).

Step3: Solve for \(x\)

Subtract 4 from both sides: \(x^{2}=20 - 4=16\). Take the square root of both sides: \(x=\sqrt{16}\).

Answer:

\(4\)