Question

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Answer 1

Step-by-step explanation:

ΔABC in which DE ∥BC and DE = 4cm, BC = 8 cm. and ar. (ΔADE) = 25 sq. cm.In ΔADE and 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

=

64

16

=

4

1

Hence, ar(ΔABC)=25×4=100sq.m