The length of the hypotenuse of a 30°–60°–90° triangle is 16. What is the perimeter? (1 point) Responses 64 + 8 64 + 8 Image with alt text: Square root 3 24 + 8 24 + 8 Image with alt text: Square root 3 16 + 64 16 + 64 Image with alt text: Square root 3 8 + 24

Answer 1

24 + 8 (Square root 3).

The perimeter of a triangle is the sum of the lengths of its three sides. In a 30°–60°–90° triangle, the sides are in the ratio 1:√3:2. Given that the hypotenuse is 16, the side opposite the 30° angle would be 8 (16 ÷ 2) and the side opposite the 60° angle would be 8√3 (8 * √3).

Therefore, the perimeter would be 8 + 8 + 8√3 = 24 + 8√3.