Question

the sides of a triangle have lengths 4, 4, and 5. what kind of triangle is it? acute right obtuse submit

Explanation:

Step1: Check for isosceles

Two sides (4,4) are equal, so it's isosceles. Now check angle type. For a triangle with sides \(a \leq b \leq c\), use \(a^2 + b^2\) vs \(c^2\). Here, \(a = 4\), \(b = 4\), \(c = 5\). Calculate \(4^2 + 4^2 = 16 + 16 = 32\), \(5^2 = 25\). Since \(32 > 25\) (\(a^2 + b^2 > c^2\)), the largest angle is acute. So the triangle is acute (and isosceles, but we check angle type here).

Step2: Confirm angle classification

In a triangle, if \(a^2 + b^2 > c^2\) (for \(c\) the longest side), the triangle is acute. Here, \(4^2 + 4^2 = 32 > 25 = 5^2\), so the largest angle is less than \(90^\circ\), making it an acute triangle. Also, two equal sides mean it's isosceles acute, but the options are acute, right, obtuse. So the answer is acute.

Answer:

acute