Question

question
find the length of the third side. if necessary, write in simplest radical form
answer
attempt 1 out of 2

Explanation:

Step1: Apply Pythagorean theorem

Let the unknown side be \(x\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = \sqrt{55}\) and \(a = 3\). So \(x^{2}+3^{2}=(\sqrt{55})^{2}\).

Step2: Simplify the equation

\(x^{2}+9 = 55\). Then \(x^{2}=55 - 9\).

Step3: Solve for \(x\)

\(x^{2}=46\), so \(x=\sqrt{46}\).

Answer:

\(\sqrt{46}\)