Question

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

Answer 1

Given: △ABC and △BDE are equilateral triangles.

D is midpoint of BC.

Since, △ABC and △BDE are equilateral triangles.

All the angles are 60∘ and hence they are similar triangles.

Ratio of areas of similar triangles is equal to ratio of squares of their sides:

Now, A(△ABC)A(△BDE)=BD2BC2

A(△BDE)A(△ABC)=BD2(2BD)2         ....Since BC=2BD

A(△BDE)A(△ABC)=4:1

Answer 2

Step-by-step explanation:

(c) 4:1 is the right answer