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Question
D and E are points on the sides AB and AC respectively of a ΔABC such that DE║BC. Find the value of x, when
AD = 4cm, DB = (x – 4) cm, AE = 8cm and EC = (3x – 19) cm.
Solution
In Δ ABC, it is given that DE ‖ BC.
Applying Thales’ theorem, we have :
`(AD)/(DB) = (AE)/(EC)`
⟹ `4/(x-4) = 8 /(3x -19)`
⟹ 4 (3x-19) = 8 (x-4)
⟹ 12x – 76 = 8x – 32
⟹ 4x = 44
⟹ x = 11 cm
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