Question

ABC and BDE are two equilateral triangle such that BD=2\3 BC. Find the ratio of area triangle ABC and BDE.

Answer 1

Given➡BD=2/3 BC
➡BC/BD=3/2
since the equilateral triangles are similar by AAA similarlity (all angles 60°)

and as we know that the areas of the two similar triangles are in the ratio of the squares of any of their corresponding sides.

therefore➡(BC/BD)^2=ar(ABC)/ar(BDE)
➡(3/2)^2= ar(ABC)/ar(BDE)
➡9/4= ar(ABC)/ar(BDE)

hence their ratio is 9:4