Question

a triangle has sides with lengths of 52 inches, 65 inches, and 39 inches. is it a right triangle? yes no

Explanation:

Step1: Recall Pythagorean theorem

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the longest side. Here, \(a = 39\), \(b = 52\), and \(c = 65\).

Step2: Calculate \(a^{2}+b^{2}\)

\(a^{2}+b^{2}=39^{2}+52^{2}=1521 + 2704=4225\)

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

\(c^{2}=65^{2}=4225\)

Step4: Compare

Since \(a^{2}+b^{2}=c^{2}\), the triangle is a right - triangle.

Answer:

yes