Inside a triangular park, there is a flower bed forming a similar triangle. Around the flower
bed runs a uniform path of such a width that the sides of the park are exactly double the
corresponding sides of the flower bed. The ratio of areas of the path to the flower bed is:

Lets assume the park is an equilateral triangle with side '2x' units, => the side of the flower bed = 'x' units

Area of park = $$\frac{\sqrt{\ 3}}{4}\cdot\left(2x\right)^2$$ =$$\frac{\sqrt{\ 3}}{4}\cdot4x^2$$

Area of flower bed = $$\frac{\sqrt{\ 3}}{4}\cdot x^2$$ 

Area of path = area of park -  area of flower bed = $$\frac{\sqrt{\ 3}}{4}\cdot3x^2$$

Ratio of area of path to area of flower bed = $$\frac{\left(\frac{\sqrt{\ 3}}{4}\cdot3x^2\right)}{\frac{\sqrt{\ 3}}{4}x^2}$$ = 3:1