Question

a triangle has sides with lengths of 14 millimeters, 47 millimeters, and 51 millimeters. is it a right triangle? yes no

Explanation:

Step1: Recall the Pythagorean theorem

For a right - triangle with side lengths \(a\), \(b\), and \(c\) (\(c\) is the longest side), \(a^{2}+b^{2}=c^{2}\). Let \(a = 14\), \(b = 47\), and \(c = 51\).

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

\(a^{2}+b^{2}=14^{2}+47^{2}=196 + 2209=2405\).

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

\(c^{2}=51^{2}=2601\).

Step4: Compare \(a^{2}+b^{2}\) and \(c^{2}\)

Since \(2405
eq2601\) (i.e., \(a^{2}+b^{2}
eq c^{2}\)).

Answer:

no