Question

a triangle has sides with lengths of 60 feet, 80 feet, and 100 feet. is it a right triangle? yes no

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with side lengths \(a\), \(b\), and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Let \(a = 60\), \(b = 80\), and \(c = 100\).

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

\(a^{2}=60^{2}=3600\), \(b^{2}=80^{2}=6400\), then \(a^{2}+b^{2}=3600 + 6400=10000\).

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

\(c^{2}=100^{2}=10000\).

Step4: Compare

Since \(a^{2}+b^{2}=c^{2}\) (i.e., \(10000 = 10000\)), the triangle is a right - triangle.

Answer:

yes