A geometry problem by Ajay Sambhriya

Geometry Level 3

The above shows 2 equilateral triangles (CME and ANF) of both side lengths 6 to be inscribed inside a rectangle ABCD but without overlapping each other.

Given that the length MN is 2, find the length AB.


The answer is 7.

Ajay Sambhriya by Ajay Sambhriya , 27, India

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2 solutions

Ajay Sambhriya
Feb 9, 2017

AB = 3 + 1 + 3 = 7

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Nice and quick visual solution!! :-D

Ojasee Duble - 4 years, 4 months ago

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thanks sir

Ajay Sambhriya - 4 years, 3 months ago
Roger Erisman
Feb 13, 2017

Drop perpendicular from F to DC at G. This forms a 30-60-90 right triangle with hypotenuse (EF) = 10.

Therefore EG which is opposite the 30 degree angle is one half of 10 or 5.

EC = 6 so GC = 6 - 5 = 1.

FB = GC = 1.

AB = AF + FB = 6 + 1 = 7

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