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Question
If D is a point on the side AB of ΔABC such that AD : DB = 3.2 and E is a Point on BC such that DE || AC. Find the ratio of areas of ΔABC and ΔBDE.
Solution
We have,
`"AD"/"DB"=3/2`
`rArr"DB"/"AD"2/3`
In ΔBDE and ΔBAC
∠B = ∠B [common]
∠ BDE = ∠A [corresponding angles]
Then, ΔBDE ~ ΔBAC [By AA similarity]
By area of similar triangle theorem
`("area"(triangleABC))/("area"(triangleBDE))="AB"^2/"BD"^2`
`=5^2/2^2` `["AD"/"DB"=3/2]`
`=25/4`
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