If the medians of two equilateral triangles are in the ratio 3: 2, then what is the ratio of their sides?
 

Median of an equilateral triangle = $\frac{\sqrt{3}}{2} \times \mathrm{side}$

Let the sides of the two equilateral triangles be a₁ and a₂ respected. Then:
$$\begin{gathered} \Rightarrow \frac{{\displaystyle \frac{\sqrt{3}}{2}{\mathrm{a}}_1}}{\frac{\sqrt{3}}{2}{\mathrm{a}}_2} = \frac{3}{2} \\ \Rightarrow \frac{{\displaystyle {\mathrm{a}}_1}}{{\mathrm{a}}_2} = \frac{3}{2} = 3 : 2 \end{gathered}$$