In the adjoining figure, `LM||AB` and if `AL=(x-3)` unit, `AC=2x` unit. `BM=(x-2)` unit and `BC=(2x+3)` unit, find the value of `x`.

Explanation

In `DeltaABC`, `LM||AB`.
`:.` by Thales theorem, `(CL)/(AL)=(CM)/(BM)`
or, `(CL+AL)/(AL)=(CM+BM)/(BM)` or, `(AC)/(AL)=(BC)/(BM)`
or, `(2x)/(x-3)=(2x+3)/(x-2)`
or, `2x^(2)-4x=2x^(2)-6x+3x-9` or, `-4x=-3x-9`
or, `-x=-9` or `x=9`
Hence the required value of `x=9`.