Question

a triangle has sides with lengths of 8 miles, 15 miles, and 20 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 \(a = 8\), \(b = 15\), and \(c = 20\) (assuming the longest side is the hypotenuse).

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

\(a^{2}+b^{2}=8^{2}+15^{2}=64 + 225=289\).

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

\(c^{2}=20^{2}=400\).

Step4: Compare

Since \(289
eq400\), i.e., \(a^{2}+b^{2}
eq c^{2}\).

Answer:

no