Last Updated on May 10, 2023
GMAT OFFICIAL GUIDE PS
Solution:
We are given a parallelogram of all equal sides, and we must determine the ratio of the length of the shorter diagonal to that of the longer diagonal. Since the sides are all equal, we know we have a rhombus, and the diagonals are perpendicular. Let’s sketch this diagram below.
We should see that the diagonals bisect each angle of the rhombus, and thus we have created four 30-60-90 right triangles. Using our side ratio of a 30-60-90 right triangle we have:
x : x√3 : 2x
Let’s use this side ratio to determine the lengths of each diagonal in terms of x.
We can see that the length of the shorter diagonal is x + x = 2x, and the length of the longer diagonal is x√3 + x√3 = 2x√3. Thus, the ratio of the length of the shorter diagonal to the length of the longer diagonal is:
(2x)/(2x√3) = 1/√3
Answer: D
