Question

a triangle has sides with lengths of 11 yards, 60 yards, and 61 yards. is it a right triangle?

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the longest side.
Let \(a = 11\), \(b = 60\), and \(c = 61\).

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

\(a^{2}+b^{2}=11^{2}+60^{2}=121 + 3600=3721\).

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

\(c^{2}=61^{2}=3721\).

Step4: Compare

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

Answer:

yes