2012-04-17 09:00:20

Triangles 1 and 2 are both equilateral triangles. If Triangle 1’s perimeter is ⅓ that of Triangle 2, and Triangle 1 has an area of 2√3 units, how long is one side of Triangle 2?

(A) 2
(B) 3
(C) 6
(D) 12
(E) 18


The correct answer is D

Explanation: Start by finding the length of one side of Triangle 1. Equilateral triangles divide into two 30°-60°-90° triangles, which have proportional sides of s:s√3:2s. However, this s is really ½ as long as the side of the equilateral triangle (since the 30-60-90 triangle is ½ the equilateral triangle), meaning that the sides are really ½s: ½s√3: s. Thus, if the height of Triangle 1 is 2√3, then the side length must be 4 (from ½s√3 = 2√3, and 2√3/ ½√3 = 4).

If the perimeter of Triangle 2 is 3 times as large as that of Triangle 1, that means that every side of Triangle 2 must be 3 times as large as every side of Triangle 1, meaning each side of Triangle 2 is just 4•3, or 12.