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If triangle Abc and triangle Bde Are Equilateral Triangles, Where D is the Mid-point of Bc, Find the Ratio of Areas of δAbc and δBde. - Mathematics

If ΔABC and ΔBDE are equilateral triangles, where D is the mid-point of BC, find the ratio of areas of ΔABC and ΔBDE.

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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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APPEARS IN

RD Sharma Class 10 Maths
Chapter 7 Triangles
Exercise 7.6 | Q 21 | Page 96
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