To determine whether the triangle with side lengths 2 inches, 5 inches, and 4 inches is acute, we need to check the relationship between the squares of its side lengths.
For a triangle to be acute, the sum of the squares of any two sides must be greater than the square of the third side for all combinations:
1. First Combination: Checking [tex]\(2^2 + 4^2\)[/tex] and [tex]\(5^2\)[/tex]:
- [tex]\(2^2 = 4\)[/tex]
- [tex]\(4^2 = 16\)[/tex]
- [tex]\(5^2 = 25\)[/tex]
- Sum of squares: [tex]\(2^2 + 4^2 = 4 + 16 = 20\)[/tex]
Here, [tex]\(2^2 + 4^2 = 20\)[/tex] is less than [tex]\(5^2 = 25\)[/tex], which means this combination does not support the triangle being acute.
Given this check, the statement that best explains the triangle being acute or not is:
- "The triangle is not acute because [tex]\(2^2 + 4^2 < 5^2\)[/tex]."
Thus, the correct answer is:
The triangle is not acute because [tex]\(2^2 + 4^2 < 5^2\)[/tex].
