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

This classification best represents an obtuse triangle, because 62 + 102 < 122, which means that the sum of the squares of the lengths of the two smaller sides is less than the square of the length of the longest side. This is the condition for an obtuse triangle. In an acute triangle, the sum of the squares of the two smaller sides is greater than the square of the longest side. Since 6 + 10 > 12, this condition is satisfied, but it is not enough to classify the triangle as acute. Therefore, the correct classification is obtuse.