The length of the hypotenuse of a 30°–60°–90° triangle is 12. What is the perimeter?
A. 6 + 18 Square root 3
B. 36 + 12 Square root 3
C. 12 + 36 Square root 3
D. 18 + 6 Square root 3
In a 30°–60°–90° triangle, the side lengths are in the ratio 1:√3:2. Therefore, in this triangle with hypotenuse 12, the shorter leg is 6 (√3 times the shorter leg) and the longer leg is 6√3 (2 times the shorter leg).
The perimeter is the sum of all three sides:
6 + 6√3 + 12 = 18 + 6√3
So the answer is (D) 18 + 6 Square root 3.