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Question
In the adjoining figure, DE is parallel to BC and AD = 1 cm, BD = 2 cm. What is the ratio of the area of ∆ABC to the area of ∆ADE?
Solution
GIVEN: DE is parallel to BC, AD = 1cm and BD = 2cm.
TO FIND: Ratio of ΔABC to area of ΔADE
According to BASIC PROPORTIONALITY THEOREM, if a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio.
In ΔABC, DE || BC.
`(AD)/(AB)=(AE)/(AC)`
`1/(2+1)=(AE)/(AC)`
`⇒ (AE)/(AC)=1/3`
So
`(ar(Δ ABC))/(ar(Δ ADE)``=((AC)/(AE))^2`
`=(3/1)^2`
`=9/1`
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