Question

find the length of the missing side of the right triangle.

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse. Here, \(c = 13\), \(a = 5\), and \(b=p\). So, \(p^{2}+5^{2}=13^{2}\).

Step2: Simplify the equation

\(p^{2}+25 = 169\). Then, \(p^{2}=169 - 25\).

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

\(p^{2}=144\).

Step4: Solve for \(p\)

Take the square root of both sides. Since \(p>0\) (length of a side), \(p=\sqrt{144}\).

Answer:

\(p = 12\)