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Question
In the given figure, AB and DE are perpendiculars to BC.
Find the ratio of the area of a ΔABC : area of ΔDEC.
Solution
In ΔABC and ΔDEC,
∠ABC = ∠DEC ...(both are right angles)
∠ACB = ∠DCE ....(common angles)
ΔABC ∼ ΔDEC ...(AA criterion for similarity)
`=> (ar (DeltaABC))/(ar (DeltaDEC)) = (AB^2)/(DE^2) = (6^2)/(4^2) = 36/16`
`=> (ar (DeltaABC))/(ar (DeltaDEC)) = 9/4`
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