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 \(c\) is the hypotenuse). Here \(c = 5\), \(a=3\), and \(b=x\). So \(3^{2}+x^{2}=5^{2}\).

Step2: Simplify the equation

\(9 + x^{2}=25\). Then \(x^{2}=25 - 9\).

Step3: Calculate \(x^{2}\)

\(x^{2}=16\).

Step4: Solve for \(x\)

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

Answer:

\(4\)