Question

In the given figure, DE DE || BCand AD:DB = 5:4 then ar(ADFE): ar(CFB)
A)25:81
B) 5: 81
C) 81 : 25
D) 22 : 88
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Answer 1

Answer:

Given ÷DE//BC

and AD:DB=5:4

To find :ar(ADFE):ar(CFB)

Solution :

ADFE&ACFB)

EDF=BCF (Alternative Interior Angles )

DEF=CBF (Alternative Interior Angles )

ByAA, DEF=CFB

ar (DEF)=(FD)

(CFB)=(BC)

In ADE&ABC

ADE=ABC

AED=ACB By Corresponding Angles

By AA, ADE&ABC

AD= DE

AB BC

5x = DE

9x BC

DE = 5

BC 9

so ( DE)/2= ( EF)/2 i.e (DE)/2 =(5)/2 = 25_

(FE) (FB) (BE) (9) 81

as (ADEF): ar (ACFB =25:81

Hence , option is correct