Question

Do the side lengths 46, 57, 67 form an acute scalene triangle?

a. Yes, they form an acute scalene triangle.
b. No, they do not form a triangle.
c. No, they form a right scalene triangle.
d. No, they form an obtuse scalene triangle.

Answer 1

The side lengths 46, 57, and 67 do not form an acute scalene triangle. They form an obtuse scalene triangle. The correct answer is option (d)

Step-by-step explanation:

To determine if the side lengths 46, 57, and 67 form an acute scalene triangle, we need to check if the sum of the squares of the two shorter sides is greater than the square of the longest side. If this condition is met, the triangle is scalene, and if all three angles are less than 90 degrees, it is also acute.

Step 1: Square the side lengths: 46^2 = 2116, 57^2 = 3249, and 67^2 = 4489.

Step 2: Check if the sum of the squares of the two shorter sides is greater than the square of the longest side: 2116 + 3249 < 4489. Since this condition is not met, the side lengths 46, 57, and 67 do not form an acute scalene triangle.

Therefore, the correct option is d. No, they form an obtuse scalene triangle.