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प्रश्न
In the following figure, DE || BC. If DE = 4 cm, BC = 6 cm and Area (ΔADE) = 16 cm2, find the area of ΔABC.
बेरीज
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उत्तर
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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