Question

Which classification best represents a triangle with side lengths 6 cm, 10 cm, and 12 cm?

acute, because 62 + 102 < 122
acute, because 6 + 10 > 12
obtuse, because 62 + 102 < 122
obtuse, because 6 + 10 > 12

Answer 1

Obtuse, because 6^2 + 10^2 = 36 + 100 = 136 < 12^2 = 144. Since the sum of the squares of the two shorter sides is less than the square of the longest side, the angle opposite the longest side is obtuse.