Question

which classification best represents a triangle with side lengths 10 in., 12 in., and 15 in?

obtuse, because
12² + 15² > 10²

acute, because
12² + 15² > 10²

acute, because
10² + 12² > 15²

obtuse, because
10² + 12² > 15²

Explanation:

Step1: Recall the triangle - classification rules

For a triangle with side lengths \(a\), \(b\), \(c\) (\(c\) is the longest side), if \(a^{2}+b^{2}>c^{2}\), the triangle is acute; if \(a^{2}+b^{2}=c^{2}\), the triangle is right - angled; if \(a^{2}+b^{2}Here, \(a = 10\), \(b = 12\), \(c = 15\) (since \(15>12>10\)).

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 \(10^{2}+12^{2}=244>15^{2}=225\).

Answer:

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