Question

Question no. 7: AABC~AADE find x
/3
A
I cm
D
E
3cm
4 cm
B
4cm
c​

Answer 1

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.

∴

ar(ΔABC)

ar(ΔADE)

=

(BC)

2

(DE)

2

⇒

ar(]DeltaABC)

25

=

(8)

2

(4)

2

=

6 4

1 6

=

4

1

Hence,

ar(ΔABC)=

25×

4=

100sq.m

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