Question

ABC and BDE are two equilateral triangles such that D is the mid point of of BC. Ratio of the areas of triangles ABC and BDE is
(a) 2:1 (b) 1:2 (c) 4:1 (d) 1:4

$choose \: the \: correct \: and \: justify \: ur \: \: answer \: \:$
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Answer 1

ar. (triangle abc)=root 3/4×cb×cb.

ar. (triangle bde)=root 3/4×bd×bd

but,

cb=2bd.

Therefore,

ar. (triangle abc)=root 3/4×2bd×2bd.

Required ratio=root 3/4×2bd×2bd/root 3/4×bd×bd.

=2 root3/2÷root3/4=4:1.

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