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Question
In the given figure, ABC is a triangle in which DE||BC. If AD = x, DB = x – 2, AE = x + 2 and EC = x – 1, then find the value of x.
Solution
In ΔABC, DE||BC
∴ `(AD)/(DB) = (AE)/(EC)` ...(By basic proportionality theorem)
`\implies x/(x - 2) = (x + 2)/(x - 1)`
`\implies` x(x – 1) = (x + 2) (x – 2)
`\implies` x2 – x = x2 – 4
`\implies` –x = –4
`\implies` x = 4
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