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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 = (7x – 4) cm, AE = (5x – 2) cm, DB = (3x + 4) cm and EC = 3x cm.
Solution
In Δ ABC, it is given that DE || BC.
Applying Thales’ theorem, we have :
`(AD)/(DB) = (AE)/(EC)`
⟹ `(7x - 4)/(3x +4) = (5x -2)/(3x)`
⟹ 3x (7x-4) = (5x-2) (3x+4)
⟹ `21x^2 – 12x = 15x^2 + 14x-8`
⟹ `6𝑥^2 – 26x + 8 = 0`
⟹ (x-4) (6x-2) =0
⟹ `x = 4,1/2`
∵ `x ≠ 1/3` (as if x = `1/3` 𝑡ℎ𝑒𝑛 𝐴𝐸 𝑤𝑖𝑙𝑙 𝑏𝑒𝑐𝑜𝑚𝑒 𝑛𝑒𝑔𝑎𝑡𝑖𝑣𝑒)
∴ x = 4 cm
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