Question

which classification best represents a triangle with side lengths 10 in., 12 in, and 15 in? acute, because 10²+12²>15² acute, because 12²+15²>10² obtuse, because 10²+12²>15² obtuse, because 12²+15²>10²

Explanation:

Step1: Recall the Pythagorean - related rules for triangles

Let \(a = 10\), \(b = 12\), and \(c = 15\) (where \(c\) is the longest side). For a triangle with side lengths \(a\), \(b\), and \(c\) (\(c\) being the longest side), if \(a^{2}+b^{2}>c^{2}\), the triangle is acute; if \(a^{2}+b^{2}

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

Calculate \(a^{2}+b^{2}\): \(10^{2}+12^{2}=100 + 144=244\). Calculate \(c^{2}\): \(15^{2}=225\).
Since \(10^{2}+12^{2}=244>225 = 15^{2}\), the triangle is acute.

Answer:

A. acute, because \(10^{2}+12^{2}>15^{2}\)