Corners are cut off from an equilateral triangle T to produce a regular hexagon H. Then, the ratio of the area of H to the area of T is
Explanation:
The hexagon will be regular only if the hexagon is symmetrical with resepect to the original triangle.
This is only possible when the corners cut are all equilateral (of let's say side x) and the side length of the hexagon is equal to side length of the equilateral corner (again x).
H = 6 × 34x2 (∵ A regular hexagon consists of six equilateral triangles of side length equal to the side length of the hexagon)
T = 34(3x)2 = 934x2 (∵ Side length of the triangle = x + x + x = 3x)
∴ HT = 69 = 23.
Hence, option (d).
» Your doubt will be displayed only after approval.
Help us build a Free and Comprehensive Preparation portal for various competitive exams by providing us your valuable feedback about Apti4All and how it can be improved.