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: Identify longest side

Longest side \(c = 15\) in.

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

\(10^2 + 12^2 = 100 + 144 = 244\).

Step3: Calculate \(c^2\)

\(15^2 = 225\).

Step4: Compare values

\(244 > 225\), so \(a^2 + b^2 > c^2\), triangle is acute.

Answer:

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