Question

a triangle has sides with lengths of 12 millimeters, 35 millimeters, and 37 millimeters. 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 \(a = 12\), \(b = 35\), and \(c = 37\).
Calculate \(a^{2}+b^{2}\):
\(a^{2}=12^{2}=144\), \(b^{2}=35^{2}=1225\)
\(a^{2}+b^{2}=144 + 1225=1369\)

Step2: Calculate \(c^{2}\)

\(c^{2}=37^{2}=1369\)
Since \(a^{2}+b^{2}=c^{2}\) (i.e., \(1369 = 1369\)), the triangle is a right - triangle.

Answer:

yes