Question

a triangle has sides with lengths of 9 centimeters, 12 centimeters, and 15 centimeters. 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 \(a = 9\), \(b = 12\), and \(c = 15\).

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

\(a^{2}+b^{2}=9^{2}+12^{2}=81 + 144=225\)

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

\(c^{2}=15^{2}=225\)

Step4: Compare

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

Answer:

yes