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

Explanation:

Step1: Identify longest side

Longest side = 5 in.

Step2: Test acute triangle rule

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

Step3: Classify the triangle

Since $2^2 + 4^2 < 5^2$, the triangle is obtuse (not acute).

Answer:

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