Question

a triangle has sides with lengths of 9 cm, 12 cm, and 15 cm. is it a right triangle? a yes b no

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with sides \(a\), \(b\), and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Let \(a = 9\), \(b = 12\), and \(c = 15\).

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

\(a^{2}+b^{2}=9^{2}+12^{2}=81 + 144=225\).

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

\(c^{2}=15^{2}=225\).

Step4: Compare results

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

Answer:

A. yes