Question

a triangle has sides with lengths of 33 inches, 52 inches, and 63 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 \(a = 33\), \(b = 52\), and \(c = 63\). Calculate \(a^{2}+b^{2}\) and \(c^{2}\).
\[a^{2}=33^{2}=33\times33 = 1089\]
\[b^{2}=52^{2}=52\times52=2704\]
\[a^{2}+b^{2}=1089 + 2704=3793\]
\[c^{2}=63^{2}=63\times63 = 3969\]

Step2: Compare results

Since \(a^{2}+b^{2}=3793
eq3969 = c^{2}\), the triangle is not a right - triangle.

Answer:

no