Question

a triangle has sides with lengths of 9 miles, 40 miles, and 41 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 \(a = 9\), \(b = 40\), and \(c = 41\).

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

\(a^{2}+b^{2}=9^{2}+40^{2}=81 + 1600=1681\)

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

\(c^{2}=41^{2}=1681\)

Step4: Compare

Since \(a^{2}+b^{2}=c^{2}\) (i.e., \(1681 = 1681\)), it is a right - triangle.

Answer:

yes