Question

Which best explains whether a triangle with side lengths 2 in., 5 in., and 4 in. is an acute triangle?

The triangle is acute because 22 + 52 > 42.
The triangle is acute because 2 + 4 > 5.
The triangle is not acute because 22 + 42 < 52.
The triangle is not acute because 22 < 42 + 52.

Answer 1

The third statement is correct.

Check: 2^2 + 4^2 = 4 + 16 = 20, and 5^2 = 25, so 2^2 + 4^2 < 5^2. Because the square of the longest side is greater than the sum of the squares of the other two, the triangle is obtuse (not acute).