In the given figure `DE||BC and AD:DB =5:4`
Find the ratio `ar (Delta DEF) : ar (Delta CFB)`

Explanation

Let `AD= 5x cm and DB= 4x cm.` then,
`AB=AD+DB=5x cm+ =9cm`
In `Delta ADE and Delta ABC`, we have
`angle ADE= angle ABC`[ corrs. `angle`]
`angle AED=angle ACB` [ corss `angle `]
`:. Delta ADE~ Delta ABC` [ by AA- similarity]
`rArr (DF)/(BC)=(AD)/(AB)=(5x)/(9x)=(5)/(9) " "...(i)`
In `Delta DEF and Delta CFB`, we have
` angle EDF= angle BCF` [ alt. int ` angle`]
and `angle DEF = angle CBF` [ alt. int. `angle`]
` :. Delta DEF ~ Delta CFB`.
`rArr (ar(Delta DEF))/(ar (Delta CFB))=(DE^(2))/(CB^(2))=(DE^(2))/(CB^(2)) =(DE^(2))/(BC^(2))=((DE)/(BC))^(2)=((5)/(9))^(2)=(25)/(81)`
`rArr ar (Delta DEF): ar (Delta CFB)= 25:81`