Ratio and proportion

The diagram shows a regular pentagon with sides of unit length. Find all the angles in the diagram. Prove that the quadrilateral shown in red is a rhombus.

Can you work out the ratio of shirt types made by a factory, if you know the ratio of button types used?

A ladder 3m long rests against a wall with one end a short distance from its base. Between the wall and the base of a ladder is a garden storage box 1m tall and 1m high. What is the maximum distance up the wall which the ladder can reach?

A square is divided into four rectangles and a square. Can you work out the ratio of the side lengths of the rectangles?

Weekly Problem 3 - 2007
What is the ratio of the area of the table covered twice, to the uncovered area?

Two perpendicular lines lie across each other and the end points are joined to form a quadrilateral. Eight ratios are defined, three are given but five need to be found.

A car with 5 tyres (four road tyres and a spare) travelled 30,000 km. All 5 tyres were used equally. How many kilometres' wear did each tyre receive?

Investigate some of the issues raised by Geiger and Marsden's famous scattering experiment in which they fired alpha particles at a sheet of gold.

What does the empirical formula of this mixture of iron oxides tell you about its consituents?