Question

If BC : CD = 2 : 3, AE : EC = 3 : 4 and BC : AE = 2 : 3, then find the ratio of the area of 'ECD to the area of 'AEB.
(1) 2 : 1
(2) 2 : 3
(3) 3 : 5
(4) 4 : 3

Answer 1

we have 3 similar triangles the main triangle : ABD two other triangles BC and ADC .
Now to find out CD we can use the later two triangles , so by similarity we have ,

BC/CA = CD/AC

which yields CD as 3.

Answer 2

Area of ∆ECD=1/2*3x*4x= 6x^2 (since it's ratio value is unknown, we take it as x).

Area of ∆ACB = 1/2*2x*7x=7x^2

Area of ∆BEC=1/2*2x*4x=4x^2

So, ∆AEB=∆ACB - ∆BEC

= (7-4)x^2= 3x^2

==>∆ECD:∆AEB= 6x^2:3x^2 = 2:1

Ans = 2:1