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Question
In the given figure, the value of x for which DE || AB is
Options
4
1
3
2
Solution
Given: In ∆ABC, DE || AB.
To find: the value of x
According to basic proportionality theorem if a line is drawn parallel to one side of a triangle intersecting the other two sides, then it divides the two sides in the same ratio.
In ∆ABC, DE || AB
`(AD)/(DB)=(AE)/(EC)`
`(x+3)/(3x+19)=(x)/(3x+4)`
`(x+3)(3x+4)=(x)=(3x+19)`
`3x^2+4x+9x+12=3x^2+19x`
`19x-13x=12`
`6x=12`
`x=2`
Hence we got the result `d`.
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