Question

a triangle has sides with lengths of 9 miles, 12 miles, and 15 miles. is it a right triangle? yes no

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, \(a^2 + b^2 = c^2\), where \(c\) is the longest side. Here, \(a = 9\), \(b = 12\), \(c = 15\).

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

\(9^2 + 12^2 = 81 + 144 = 225\)

Step3: Calculate \(c^2\)

\(15^2 = 225\)

Step4: Compare results

Since \(9^2 + 12^2 = 15^2\) (225 = 225), the triangle satisfies the Pythagorean theorem.

Answer:

yes