Question

a triangle has sides with lengths of 32 miles, 40 miles, and 24 miles. 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 \(a = 24\), \(b = 32\), and \(c = 40\).

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

\(a^{2}=24^{2}=24\times24 = 576\), \(b^{2}=32^{2}=32\times32 = 1024\).
\(a^{2}+b^{2}=576 + 1024=1600\).

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

\(c^{2}=40^{2}=40\times40 = 1600\).

Step4: Compare \(a^{2}+b^{2}\) and \(c^{2}\)

Since \(a^{2}+b^{2}=1600\) and \(c^{2}=1600\), \(a^{2}+b^{2}=c^{2}\).

Answer:

yes