Question

a triangle has sides with lengths of 27 kilometers, 36 kilometers, and 45 kilometers. is it a right triangle? yes no

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with side lengths \(a\), \(b\), and \(c\) (\(c\) being the longest side), \(a^{2}+b^{2}=c^{2}\). Here \(a = 27\), \(b = 36\), and \(c = 45\).

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

\(a^{2}+b^{2}=27^{2}+36^{2}=729 + 1296=2025\).

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

\(c^{2}=45^{2}=2025\).

Step4: Compare

Since \(a^{2}+b^{2}=c^{2}\) (i.e., \(2025 = 2025\)), the triangle is a right - triangle.

Answer:

yes