Question

the sides of a triangle have lengths 2, 13, and 12. what kind of triangle is it? acute right obtuse

Explanation:

Step1: Recall the Pythagorean - related inequalities

Let \(a = 2\), \(b = 12\), and \(c = 13\) (where \(c\) is the longest side). For a triangle with side - lengths \(a\), \(b\), \(c\) (\(c\) being the longest side):
If \(a^{2}+b^{2}=c^{2}\), the triangle is a right - triangle.
If \(a^{2}+b^{2}>c^{2}\), the triangle is an acute - triangle.
If \(a^{2}+b^{2}

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

Calculate \(a^{2}=2^{2}=4\), \(b^{2}=12^{2}=144\), so \(a^{2}+b^{2}=4 + 144=148\).
Calculate \(c^{2}=13^{2}=169\).

Step3: Compare \(a^{2}+b^{2}\) and \(c^{2}\)

Since \(148<169\), that is \(a^{2}+b^{2}

Answer:

obtuse