Question

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

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 \(c = 7\), \(b=\sqrt{13}\), and \(a=x\). So \(x^{2}+(\sqrt{13})^{2}=7^{2}\).

Step2: Simplify the equation

\(x^{2}+13 = 49\). Then \(x^{2}=49 - 13\).

Step3: Solve for \(x\)

\(x^{2}=36\), so \(x=\sqrt{36}=6\).

Answer:

\(6\)