Question

a triangle has sides with lengths of 21 miles, 60 miles, and 67 miles. is it a right triangle? yes no

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with sides \(a\), \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Let \(a = 21\), \(b = 60\) and \(c = 67\).

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

\(a^{2}+b^{2}=21^{2}+60^{2}=441 + 3600=4041\)

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

\(c^{2}=67^{2}=4489\)

Step4: Compare

Since \(4041
eq4489\), i.e., \(a^{2}+b^{2}
eq c^{2}\).

Answer:

no