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.

Answer 1

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`