Question

The length of the hypotenuse of a 30°-60°-90° triangle is 12. What is the perimeter?

A. 6 + 18 √3
B. 36 + 12 √3
C. 12 + 36 √3
D. 18 + 6 √3

Answer 1

In a 30°-60°-90° triangle the hypotenuse (c) is twice the length of the shorter side (a):

So a = 12/2 = 6

The longer side (b) is equal to the shorter side multiplied by √3:

So b = 6√3

The three side lengths are:

a = 6

b = 6√3

c = 12

The perimeter is the sum of the 3 sides:

Perimeter = 6 + 6√3 + 12 = 18 + 6√3

The answer is D.