Question

a triangle has sides with lengths of 21 inches, 72 inches, and 75 inches. is it a right triangle? yes no

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the longest side.
Let \(a = 21\), \(b = 72\), and \(c = 75\).
Calculate \(a^{2}+b^{2}\):
\(a^{2}=21^{2}=441\), \(b^{2}=72^{2}=5184\).
Then \(a^{2}+b^{2}=441 + 5184=5625\).

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

\(c^{2}=75^{2}=5625\).
Since \(a^{2}+b^{2}=c^{2}\) (\(5625 = 5625\)), the triangle is a right - triangle.

Answer:

yes