Question

In the adjoining figure, in triangle ABC, seg DE II side BC, DE 2 BC 3 A(triangle ADE)= 32 cm2 find the area of BCED

Answer 1

If ADE is any triangle and BC is drawn parallel to DE, then  AD/BD  =  AE/CE;

and triangles  ADE and ABC are similar  with common angle A ;

Let F is mid point of DE , and G is midpoint of BC

AF = height of triangle ADE;

AG=height of triangle ABC;

so DE/BC=AF/AG

=>2/3=AF/AG ......eqn1;

=>Area of ADE= 32 cm2 =1/2*AF*DE

=>AF=32cm;

=>so  in eqn 1;

AG=48cm;

=> Area of ABC=1/2*AG*BC=72cm2 ....Ans.