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Question
In the given figure, DE || BC in ∆ABC such that BC = 8 cm, AB = 6 cm and DA = 1.5 cm. Find DE.
Solution
Given: In ∆ABC, DE || BC. BC = 8 cm, AB = 6 cm and DA = 1.5 cm.
To find: DE
In ∆ABC and ∆ADE
\[\angle B = \angle ADE \left( \text{Corresponding angles} \right)\]
\[\angle A = \angle A \left( \text{Common} \right)\]
\[ \therefore ∆ ABC~ ∆ ADE \left( \text{AA Similarity} \right)\]
so,
`(BC)/(DE)=(AB)/(DA)`
`8/(DE)=6/1.5`
`DE= (8xx1.5)/6`
`DE= 2cm`
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