Question

Please solve q 89?

Answer 1

option (3) `8cm^2`

Explanation:

Given area of `Delta ABC=10cm^2`

`AD =2cm and BD =3cm`, So `AB=5cm`

Area of `Delta ABE=` area of quadrilateral DBEF

Area of `Delta ABE-DeltaBDE=` area of quadrilateral DBEF-`Delta BDE`

Area of `Delta ADE=Delta DFE`

But `Delta ADE and Delta DFE` lie on same base `DE`. So their heights will be same. Hence `DE"||"AC`

So `Delta ABC and Delta BDE` are similar

Hence

`(Delta BDE)/(Delta ABC)=(BD)^2/(AB)^2=3^2/5^2=9/25`

`Delta BDE=9/25xxDelta ABC=9/25xx10=18/5cm^2`

Again

`(DeltaADE)/(DeltaBDE)=(AD)/(BD)=2/3`

`=>(DeltaADE+DeltaBDE)/(DeltaBDE)=2/3+1=5/3`

`Delta ABE=5/3xxDelta BDE=5/3xx18/5=6cm^2`