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Ratio of perimeter and area with weird angle condition

Source: Tuymaada 2020 Senior, Problem 3 (Junior, P4)

October 6, 2020

ratiogeometryperimeter

Problem Statement

Points

D

and

E

lie on the lines

BC

and

AC

respectively so that

B

is between

C

and

D

C

is between

A

and

E

BC = BD

and

\angle BAD = \angle CDE

. It is known that the ratio of the perimeters of the triangles

ABC

and

ADE

2

. Find the ratio of the areas of these triangles.