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Question
If ΔABC and ΔBDE are equilateral triangles, where D is the mid-point of BC, find the ratio of areas of ΔABC and ΔBDE.
Solution
We have,
ΔABC and ΔBDE are equilateral triangles then both triangles are equiangular
∴ ΔABC ~ ΔBDE [By AAA similarity]
By area of similar triangle theorem
`("area"(triangleABC))/("area"(triangleBDE))="BC"^2/"BD"^2`
`=(2"BD")^2/"BD"^2` [D is the mid-point of BC]
`=(4"BD"^2)/"BD"^2`
`=4/1`
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