Question

a triangle has sides with lengths of 72 meters, 97 meters, and 65 meters. 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.
Let \(a = 65\), \(b = 72\), and \(c = 97\).
Calculate \(a^{2}+b^{2}\):
\(a^{2}=65^{2}=65\times65 = 4225\)
\(b^{2}=72^{2}=72\times72 = 5184\)
\(a^{2}+b^{2}=4225 + 5184=9409\)

Step2: Calculate \(c^{2}\)

\(c^{2}=97^{2}=97\times97 = 9409\)
Since \(a^{2}+b^{2}=c^{2}\) (i.e., \(9409 = 9409\)).

Answer:

yes