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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
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