The length of the hypotenuse of a 30°–60°–90° triangle is 16. What is the perimeter? (1 point) Responses

64 + 8: Square root 3

24 + 8: Square root 3

16 + 64: Square root 3

8 + 24: square root 3

1 answer

24 + 8: Square root 3

The hypotenuse of a 30°–60°–90° triangle is twice the length of the shorter leg. Therefore, the shorter leg is 8, and the longer leg is 8 times the square root of 3.

The perimeter of the triangle is the sum of all three sides, so it would be 8 + 16 + 8 square root 3, which simplifies to 24 + 8 square root 3.