Question

a triangle has sides with lengths of 5 millimeters, 12 millimeters, and 13 millimeters. is it a right triangle?

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the longest side.
Let \(a = 5\), \(b = 12\), and \(c = 13\).

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

\(a^{2}+b^{2}=5^{2}+12^{2}=25 + 144=169\)

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

\(c^{2}=13^{2}=169\)

Step4: Compare

Since \(a^{2}+b^{2}=c^{2}\) (i.e., \(169 = 169\)), it is a right - triangle.

Answer:

yes