Question

a triangle has sides with lengths of 13 kilometers, 84 kilometers, and 85 kilometers. 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, \(a = 13\), \(b = 84\), \(c = 85\).

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

\(13^2 + 84^2 = 169 + 7056 = 7225\)

Step3: Calculate \(c^2\)

\(85^2 = 7225\)

Step4: Compare results

Since \(13^2 + 84^2 = 85^2\), the triangle satisfies the Pythagorean theorem.

Answer:

yes