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

For a triangle with side lengths \(a\), \(b\), and \(c\) (\(c\) being the longest side), if \(a^{2}+b^{2}=c^{2}\), it's a right - triangle; if \(a^{2}+b^{2}>c^{2}\), it's an acute - triangle; if \(a^{2}+b^{2}Here, \(a = 10\), \(b = 12\), and \(c = 15\).

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 \(10^{2}+12^{2}=244>15^{2}=225\), the triangle is acute.

Answer:

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