Question

a triangle has sides with lengths of 14 millimeters, 48 millimeters, and 50 millimeters. is it a right triangle?

Explanation:

Step1: Apply the Pythagorean theorem

The Pythagorean theorem for a right - triangle is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the longest side. Let \(a = 14\), \(b = 48\), and \(c = 50\).
Calculate \(a^{2}+b^{2}\):
\(14^{2}+48^{2}=196 + 2304\)
\(=2500\)
Calculate \(c^{2}\):
\(50^{2}=2500\)

Step2: Compare the two results

Since \(14^{2}+48^{2}=50^{2}\) (i.e., \(2500 = 2500\))

Answer:

yes