Question

1. according to the pythagorean theorems converse, if (a = 5), (b = 12), and (c = 13), what type of triangle is it? a. right triangle b. equilateral triangle c. acute triangle d. obtuse triangle

Explanation:

Step1: Recall Pythagorean Theorem's converse

The converse states that if \(a^{2}+b^{2}=c^{2}\) in a triangle with side - lengths \(a\), \(b\), and \(c\) (\(c\) being the longest side), then the triangle is a right - triangle.

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

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

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

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

Step4: Compare \(a^{2}+b^{2}\) and \(c^{2}\)

Since \(a^{2}+b^{2}=169\) and \(c^{2}=169\), we have \(a^{2}+b^{2}=c^{2}\).

Answer:

A. Right triangle