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Question

# ABCD is a square. Equilateral triangles ACF and ABE are drawn on the the diagonal AC and side AB respectively. Find area of △ACF : area of △ABE.

A

2:1

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B

2:1

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C

4:1

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D

8:1

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Solution

## The correct option is B 2:1 Let the length of AB be a units. .....(i) We know that diagonal of a square =√2× side length ⇒AC=√2×AB⇒AC=√2a....(ii) Now, △ ABE and △ ACF are equilateral triangles. Each angle of both △ ABE and △ ACF is 60∘. ∴△ABE∼△ ACF (by AAA similarity criterion) So, from (i) and (ii), we can conclude that, ar(ACF)ar(ABE)=AC2AB2=2a2a2=21

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