Question

a triangle has sides with lengths of 32 centimeters, 60 centimeters, and 66 centimeters. 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.

Step2: Identify the sides

Let \(a = 32\), \(b = 60\), and \(c = 66\). Calculate \(a^{2}+b^{2}\) and \(c^{2}\).
\[a^{2}=32^{2}=32\times32 = 1024\]
\[b^{2}=60^{2}=60\times60=3600\]
\[a^{2}+b^{2}=1024 + 3600=4624\]
\[c^{2}=66^{2}=66\times66 = 4356\]

Step3: Compare

Since \(a^{2}+b^{2}=4624\) and \(c^{2}=4356\), and \(a^{2}+b^{2}
eq c^{2}\).

Answer:

no