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 the unknown side be \(x\). Here, \(c = 2\sqrt{5}\), \(a = 4\), and \(b=x\). Then \(x^{2}+4^{2}=(2\sqrt{5})^{2}\).

Step2: Simplify the equation

Expand the terms: \(x^{2}+16 = 4\times5\). So \(x^{2}+16=20\).

Step3: Solve for \(x^{2}\)

Subtract 16 from both sides: \(x^{2}=20 - 16\). Then \(x^{2}=4\).

Step4: Find \(x\)

Take the square root of both sides. Since length is non - negative, \(x=\sqrt{4}\).

Answer:

\(2\)