The point `D` and `E` are situated on the sides `AB` and `AC` of `DeltaABC` in such a way that `DE||BC` and `AD : DB=3 :1`, If `EA=3.3cm`, then the length of `AC` is

Options

A. `1.1cm`
B. `4cm`
C. `4.4cm`
D. `5.5cm`

Explanation

`:'` in `DeltaABC`, `DE||BC`,
`:.` by Thales' theorem we get, `(AD)/(BD)=(AE)/(CE)` or, `(BD)/(AD)=(CE)/(AE)`
or, `(BD+AD)/(AD)=(CE+AE)/(AE)`
or, `(4)/(3)=(AC)/(3.3)` [`:'AD:DB=3:1` or, `(BD)/(AD)=(1)/(3)` or, `3AC=4xx3.3` or, `(AD+BD)/(AD)=(3+1)/(3)=(4)/(3)`]
or, `AC=(4xx3.3)/(3)` or, `AC=4.4`
`:.AC=4.4cm`, `:. (c )` is correct.