A line parallel to the side `BC` of `DeltaABC` intersects the sides `AB` and `AC` at the points `x` and `Y` respectively. If `AX=2.4cm`, `AY=3.2cm` and `YC=4.8cm`, then the length of `AB` is

Options

A. `3.6cm`
B. `6cm`
C. `6.4cm`
D. `7.2cm`

Explanation

`:'` the side `BC` of `DeltaABC` is parallel to `XY` and `XY` intersects `AB` and `AC` at `X` and `Y` respectively.
`:.` by Thales' theorem,
`(AX)/(BX)=(AY)/(CY)`, or `(BX)/(AX)=(CY)/(AY)` or, `(BX+AX)/(AX)=(CY+AY)/(AY)`
or, `(AB)/(2.4)=(4.8+3.2)/(3.2)`
[`:' AX=2.4cm`, `AY=3.2cm` and `CY=4.8cm`]
or, `(AB)/(2.4)=(8)/(3.2)` or, `AB=(8xx2.4)/(3.2)=6`
`:. AB=6cm` `:.` `(b)` is correct