# Problem of the Week Problem D Coloured Areas

Chandra wishes to paint a sign. The sign is composed of three concentric semi-circles, creating an outer band, a middle band, and an inner semi-circle.

The outer band is divided into five regions of equal area and will be painted blue. Each of these regions is labelled with a $$B$$. The middle band is divided into three regions of equal area and will be painted red. Each of these regions is labelled with an $$R$$. The inner semi-circle will be painted white.

The diameter of the largest semi-circle is $$10$$ m and the diameter of the middle semi-circle is $$6$$ m.

If the ratio of the area of one region marked with an $$R$$ to the area of one region marked with a $$B$$ is $$5:6$$, what is the diameter of the inner semi-circle?