Question

triangle classification theorems
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 $2^2 + 5^2 > 4^2$.
the triangle is not acute because $2^2 < 4^2 + 5^2$
the triangle is not acute because $2^2 + 4^2 < 5^2$
the triangle is acute because $2 + 4 > 5$.

Explanation:

Step1: Identify longest side

Longest side = 5 in.

Step2: Apply acute triangle test

For acute triangles, sum of squares of two shorter sides > square of longest side:
$2^2 + 4^2 = 4 + 16 = 20$
$5^2 = 25$

Step3: Compare values

$20 < 25$, so $2^2 + 4^2 < 5^2$. This means the triangle is obtuse, not acute.

Answer:

The triangle is not acute because $2^2 + 4^2 < 5^2$.