Question

using a = 20, b = 15 and c = 25, is triangle abc a right triangle?

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (the longest side).

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

Given \(a = 20\), \(b = 15\), then \(a^{2}=20^{2}=400\), \(b^{2}=15^{2}=225\), and \(a^{2}+b^{2}=400 + 225=625\).

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

Given \(c = 25\), then \(c^{2}=25^{2}=625\).

Step4: Compare

Since \(a^{2}+b^{2}=c^{2}\) (i.e., \(625 = 625\)), the triangle is a right - triangle.

Answer:

Yes