Question

a triangle has sides with lengths of 22 inches, 32 inches, and 40 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 \(a = 22\), \(b = 32\), and \(c = 40\).
Calculate \(a^{2}+b^{2}\):
\(a^{2}=22^{2}=484\), \(b^{2}=32^{2}=1024\).
\(a^{2}+b^{2}=484 + 1024=1508\).
Calculate \(c^{2}\):
\(c^{2}=40^{2}=1600\).

Step2: Compare results

Since \(a^{2}+b^{2}=1508
eq1600 = c^{2}\), the triangle is not a right - triangle.

Answer:

no