kkahuja91 wrote:
A window is in the shape of a regular hexagon with each side of length 80 Centimeters. If a diagonal through the center of the hexagon is W centimeters long, then w =?
(A) 80
(B) 120
(C) 150
(D) 160
(E) 240
Attachment:
Solution.png [ 8.02 KiB | Viewed 14572 times ]
Let us draw a regular hexagon ABCDEF, as in figure above. We need to find the length of the diagonal BE.
Given: It is a regular hexagon so, AB = BC = CD = DE = EF = AF = 80 cm and each angle is 120
Join BF and CE, making BCEF a rectangle. Angle BCE = 90
As the diagonal BE bisects angles ABC and DEF, angle CBE is 60. So, triangle BCE is a 30-60-90 triangle and the sides of this triangle is in the ratio - \(1:\sqrt{3}:2\)
Hence, BE = 160
Answer - D.