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Question
In ΔABC, D and E are points on the sides AB and AC respectively such that DE || BC
If AD = x, DB = x − 2, AE = x + 2 and EC = x − 1, find the value of x.
Solution
We have,
DE || BC
Therefore, by basic proportionality theorem,
We have,
`"AD"/"DB"="AE"/"EC"`
`rArrx/(x-2)=(x+2)/(x-1)`
⇒ x(x − 1) = (x + 2)(x − 2)
⇒ x2 − x = x2 − (2)2 [∵ (a – b) (a + b) = a2 − b2]
⇒ −x = −4
⇒ x = 4 cm
∴ x = 4 cm
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