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Question
In the following figure, point D divides AB in the ratio 3 : 5. Find :
DE = 2.4 cm, find the length of BC.
Solution
Given that `(AD)/(DB) = 3/5`
So, `(AD)/(AB) = 3/8`
In ΔADE and ΔABC,
∠ADE = ∠ABC ...(Since DE || BC, so the angles are corresponding angles)
∠A = ∠A ...(Common angle)
∴ ΔADE ∼ ΔABC ...(AA criterion for similarity)
`=> (AD)/(AB) = (DE)/(BC)`
`=> 3/8 = (2.4)/(BC)`
`=>` BC = 6.4 cm
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