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Question
In the given figure, DE || BC and \[AD = \frac{1}{2}BD\]. If BC = 4.5 cm, find DE.
Solution
Given: In ∆ABC, DE || BC. `AD = 1/2BD` and BC = 4.5 cm.
To find: DE
In ∆ABC and ∆ADE
\[\angle B = \angle ADE \left( \text{Corresponding angles} \right)\]
\[\angle A = \angle A \left( \text{Common} \right)\]
\[ \therefore ∆ ABC~ ∆ ADE \left( \text{AA Similarity} \right)\]
`(AD)/(AB)=(DE)/(BC)`
`(AD)/(AD+BD)=(DE)/(BC)`
`(1/2BD)/(1/2+BD+BD)=(DE)/(BC)`
`1/3=(DE)/(BC)`
`1/3=(DE)/4.5`
`DE=1.5 cm`
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