Question

a triangle has sides with lengths of 72 centimeters, 97 centimeters, and 65 centimeters. is it a right triangle? yes no

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with sides \(a\), \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Let \(a = 65\), \(b = 72\) and \(c = 97\).

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

\(a^{2}+b^{2}=65^{2}+72^{2}=4225 + 5184=9409\).

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

\(c^{2}=97^{2}=9409\).

Step4: Compare

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

Answer:

yes