Question

a triangle has sides with lengths of 18 miles, 80 miles, and 82 miles. 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 \(a = 18\), \(b = 80\), and \(c = 82\).

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

\(a^{2}+b^{2}=18^{2}+80^{2}=324 + 6400=6724\).

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

\(c^{2}=82^{2}=6724\).

Step4: Compare

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

Answer:

yes