Question

a triangle has sides with lengths of 30 inches, 72 inches, and 78 inches. 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 \(a = 30\), \(b = 72\) and \(c = 78\).

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

\(a^{2}+b^{2}=30^{2}+72^{2}=900 + 5184=6084\)

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

\(c^{2}=78^{2}=6084\)

Step4: Compare

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

Answer:

yes