Question

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

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with sides \(a\), \(b\) and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Let \(a = 27\), \(b = 36\) and \(c = 45\).

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

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

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

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

Step4: Compare

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

Answer:

yes