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Question
D and E are points on the sides AB and AC respectively of a ΔABC such that DE║BC.
If` (AD)/(AB) = 8/15 and EC = 3.5cm`, find AE.
Solution
In Δ ABC, it is given that DE ‖ BC.
Applying Thales’ theorem, we get:
`(AD)/(AB) = (AE)/(AC)`
⟹ `8/15 = (AE)/(AE + EC)`
⟹ `8/15 = (AE)/(AE + 3.5)`
⟹ 8AE + 28 = 15AE
⟹ 7AE = 28
⟹ AE = 4cm
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