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triangleABC and triangleBDE are two equi...

`triangleABC and triangleBDE` are two equilateral triangles such that D is the midpoint of BC. Then, `ar(triangleBDE): ar(triangleABC)` = ?

A

`1 : 2`

B

`1 : 4`

C

`sqrt3 : 2`

D

`3 : 4`

Text Solution

Verified by Experts

The correct Answer is:
B
Let BC = a Then, `BD = (a)/(2)`.
`therefore (ar(triangleBDE))/(ar(triangleABC))=((sqrt3)/(4)*((a)/(2))^(2))/((sqrt3)/(4)*a^(2))=(1)/(4)`.
So, the required ratio is `1 : 4`.
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