The shortest way for those who dont know the formula [

Ratio of Area of two similar triangles = Square of ratio of their correcponding sides]

But I doubt this question....as Option A and E are same.

Two step procedure..

Area of triangle= Area of quad

Area of Traiangle ADE= \sqrt{3} *25/4.

Area of Quad= 25* \sqrt{3} /4

Implies Area of bigger equilateral triangle = 50 \sqrt{3}/4

Apply Area of Equilateral again= you will get, AC=AB= 5 \sqrt{2}.

so DB= 5\sqrt{2}-5 => You will get Option A, which is nothing but Option E.

Please let me know if I am wrong.

reto wrote:

Attachment:

T8892.png

Both triangles ABC and ADE are equilateral. The shaded area enclosed in BCED is equal to the area of ΔADE. If AE=5, what is the length of BD?

A. \(5*(\sqrt{2}-1)\)

B. \(2*\sqrt{5}\)

C. 3

D. \(5*(2-\sqrt{2})\)

E. \(\frac{5}{\sqrt{2}+1}\)

Do you mind solving withouth doing the maths?
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Kudos to you, for helping me with some KUDOS.