Question

a triangle has sides with lengths of 24 inches, 32 inches, and 40 inches. is it a right triangle?

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the longest side. Let \(a = 24\), \(b = 32\), \(c = 40\).
Calculate \(a^{2}+b^{2}\):
\(24^{2}+32^{2}=576 + 1024\)
\(=1600\)
Calculate \(c^{2}\):
\(40^{2}=1600\)

Step2: Compare results

Since \(24^{2}+32^{2}=40^{2}\) (i.e., \(1600 = 1600\))

Answer:

Yes