Question

a triangle has sides with lengths of 85 meters, 36 meters, and 77 meters. is it a right triangle? yes no

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with side lengths \(a\), \(b\), and \(c\) (where \(c\) is the hypotenuse, the longest side), \(a^{2}+b^{2}=c^{2}\). Here, \(a = 36\), \(b = 77\), and \(c = 85\).

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

\(a^{2}+b^{2}=36^{2}+77^{2}=1296 + 5929=7225\)

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

\(c^{2}=85^{2}=7225\)

Step4: Compare results

Since \(a^{2}+b^{2}=c^{2}\) (i.e., \(7225 = 7225\)), the triangle is a right - triangle.

Answer:

yes