boomgoesthegmat wrote:
The parallelogram shown has four sides of equal length. What is the ratio of the length of the shorter diagonal to the length of the longer diagonal?
A) 1/2
B) 1/root2
C) 1/2root2
D) 1/root3
E) 1/2root3
OA:
D
Assume the length of each side = x
The other angles would be 60, 120 and 120.
Diagonal divides the parallelogram into half
Hence the shorter diagonal will make two equilateral triangles
Length of the shorter diagonal = length of side = x
For the longer diagonal.
The diagonal will divide the parallelogram in to isosceles triangles with angles 30, 120, 30
Dropping a perpendicular from top most point on to the diagonal, we have two triangles with angles 30, 60 and 90 with base as half the length of diagonal
Hypotenuse = x,
Cos 30 = base/x
base = (√3/2)*x
Hence the length of the diagonal = √3x
Ratio of the shorter to the longer diagonal = x : √3x = 1: √3
Correct Option:
D
