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Find the value of x for which DEabs()AB ...

Find the value of x for which DE`abs()`AB in given figure.

A

`1`

B

`3`

C

`4`

D

`2`

Text Solution

Verified by Experts

The correct Answer is:
D
Given, `DEabs()AB`
`therefore (CD)/(AD)=(CE)/(BE)` [by basic proportionality theorem]
`rArr (x+3)/(3x+19)=x/(3x+4)`
`rArr (x+3)(3x+4)=x(3x+19)`
`rArr 3x^(2)+4x+9x+12=3x^(2)+19x`
`rArr 19x-13x=12`
`rArr6x=12`
`therefore x=12/6=2`
Hence, the required value of x is 2.
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