Question

a triangle has sides with lengths of 5 miles, 12 miles, and 13 miles. is it a right triangle?

Explanation:

Step1: Recall Pythagorean theorem

For a right triangle, the sum of the squares of the two shorter sides should equal the square of the longest side. The formula is \(a^2 + b^2 = c^2\), where \(c\) is the longest side.

Step2: Identify sides

Here, the sides are 5, 12, 13. The longest side \(c = 13\), and the other two \(a = 5\), \(b = 12\).

Step3: Calculate squares

\(a^2 = 5^2 = 25\), \(b^2 = 12^2 = 144\), \(c^2 = 13^2 = 169\).

Step4: Check Pythagorean theorem

Sum of \(a^2\) and \(b^2\) is \(25 + 144 = 169\), which equals \(c^2\).

Answer:

yes