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Question
In Figure, DE || BC If DE = 4 cm, BC = 6 cm and Area (ΔADE) = 16 cm2, find the area of ΔABC.
Solution
We have, DE || BC, DE = 4 cm, BC = 6 cm and area (Δ𝐴𝐷𝐸) = 16 cm2
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`
`rArr16/("Area"(triangleABC))=4^2/6^2`
⇒ Area (ΔABC) = `(16xx36)/16=36"cm"^2`
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