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

Hi,

Answer C 2²+4² < 5²

Explanation:

In a acute triangle, the square of the longest side is less than the sum of the squares of two smaller sides.

Here :

2²+4²=20

5²=25

25 is not less then 20: the triangle is NOT an acute triangle.

(proof : there is an angle of 108.21°)