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

The Pythagoras theorem states that
the sum of squares of the shorter sides (legs) of a right triangle equals the square of the third side.

A corollary from the same theorem helps us solve this problem:
If the sum of the squares of the shorter sides of a triangle is greater than the square of the third side, the included angle is acute.  ..... (case 1)
Conversely, if the sum of the squares of the shorter sides of a triangle is less than the square of the third side, the triangle is obtuse.  .....(case 2)

Here we have
6^2+10^2 = 36+100=136 <12^2=144
Therefore case 2 applies, and the triangle is obtuse.

Answer 2

The answer is C, xotwod