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In the given figure overline(DE)||overli...

In the given figure `overline(DE)||overline(AC)`. Find the value of x.
`(a) 1 (b) 2 (c) 3 (d) 4`

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Verified by Experts

In `angle ABC`,
`DE|| AC`
`therefore (BD)/(DA)=(BE)/(EC)` (Basic proportionality theorem)
` rArr (2x+10)/(3x)=(x+7)/(2x)`
`rArr2x(2x+10)=3x(x+7)`
`rArr 4x^2+20x=3x^2+21x`
`rArr x^2-x=0`
`rArrx(x-1)=0`
`rArrx-1=0`
`rArrx=1`
`therefore` Hence, option (a) is the correct answer.
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