Question

using a = 5, b = 12 and c = 13, is triangle abc a right angle triangle? yes no

Explanation:

Step1: Recall Pythagorean theorem

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

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

Given \(a = 5\), \(b = 12\), then \(a^{2}+b^{2}=5^{2}+12^{2}=25 + 144=169\).

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

Given \(c = 13\), then \(c^{2}=13^{2}=169\).

Step4: Compare

Since \(a^{2}+b^{2}=c^{2}\) (i.e., \(169 = 169\)), the triangle is a right - triangle.

Answer:

Yes