In the adjoining figure, $\mathrm{PQ}\parallel \mathrm{CA}$ and all lengths are given in centimetres. This length BC is 

 

In the adjoining figure, $\mathrm{MN}\parallel \mathrm{QR}.$ If $\mathrm{PN}=3.6\mathrm{cm}$ $\mathrm{NR}=2.4\mathrm{cm}\text{ and }\mathrm{PQ}=5\mathrm{cm}$, then $\mathrm{PM}$ is 

If the area of two similar triangles are in the ratio $4 : 9$, then their corresponding sides are in the ratio

If $ABC$ and $BDE$ are two equilateral triangles such that $D$ is mid-point of $BC$, then the ratio of the areas of triangles $ABC$ and $BDE$ is