The length of the hypotenuse of a 30 - 60 - 90 triangle is 16. What is the perimeter?

A. 64+8 square root of 3

B. 24+8 square root of 3

C. 16+64 square root of 3

D. 8+24 square root of 3

For a Right triangle with 30-60-90 degrees, the sides have specific ratios. If we assign a length of 1 to the short side (opposite 30), the hypotenuse will be 2, and the other leg will be square root 3.

Given that the hypotenuse is 16 in this triangle, we will need to multiply each of our ratios given above by 8 (16/2)

So, the short side is 8, the hypotenuse is 16 and the last leg is 8 (square root 3). Adding these three sides we get

8 + 16 + 8 sqrt (3)

24 + 8 sqrt (3)

The answer is B