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Question
In Figure, DE || BC If DE = 4cm, BC = 8 cm and Area (ΔADE) = 25 cm2, find the area of ΔABC.
Solution
We have, DE || BC, DE = 4 cm, BC = 8 cm and area (ΔADE) = 25cm2
In ΔADE and ΔABC
∠A = ∠A [Common]
∠ADE = ∠ABC [Corresponding angles]
Then, ΔADE ~ ΔABC [By AA similarity]
By area of similar triangle theorem
`("Area"(triangleADE))/("Area"(triangleABC))="DE"^2/"BC"^2`
`rArr25/("Area"(triangleABC))=4^2/8^2`
⇒ Area (ΔABC) = `(25xx64)/16=100"cm"^2`
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