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: Recall the condition for an acute triangle

For a triangle with side lengths \(a\), \(b\), \(c\) (\(c\) is the longest side), the triangle is acute if \(a^{2}+b^{2}>c^{2}\), right - angled if \(a^{2}+b^{2}=c^{2}\), and obtuse (not acute) if \(a^{2}+b^{2}Here, the side lengths are \(2\), \(4\), \(5\), and \(c = 5\) (the longest side), \(a = 2\), \(b = 4\).

Step2: Calculate \(a^{2}+b^{2}\) and \(c^{2}\)

Calculate \(a^{2}+b^{2}\): \(2^{2}+4^{2}=4 + 16=20\)
Calculate \(c^{2}\): \(5^{2}=25\)
Since \(20<25\) (i.e., \(2^{2}+4^{2}<5^{2}\)), the triangle is not acute.

Answer:

The triangle is not acute because \(2^{2}+4^{2}<5^{2}\).