Question

In the given figure, DE || BC. DE = 4 cm, BC = 8 cm,
area of triangleADE = 25 sq cm. Find the area of triangleABC.

​

Answer 1

$\huge \pink {answeR}$

ΔABCin which DE

∥

BC

and DE = 4cm, BC = 8 cm. and ar. (

ΔADE

) = 25 sq. cm.InΔADEand ΔABC

∠A=

∠A

[Common]

∠ADE=

∠ABC

[Corresponding angles]

∠ADE=

∠ACB

[Corresponding angles]

∴

ΔADE∼

ΔABC

[AAA similarity]

Since ratio of areas of two similar

Δs

is equal to ratio of squares on the corresponding sides.

∴

a r ( Δ A B C )

a r ( Δ A D E )

=

( B C ) 2

( D E ) 2

⇒

ar(]DeltaABC)

25

=

( 8 ) 2

( 4 ) 2

=

6 4

1 6

=

4

1

Hence,

ar(ΔABC)=

25×

4=

100sq.m