Stage: 4 Challenge Level: 
Triangle ABC is an equilateral triangle and the three lines marked with arrows in the diagram are parallel. If the perpendicular distances between the parallel lines are 1 unit and 2 units then calculate the length of the sides of the triangle. Suppose the distances between the parallel lines are a units and b units then what is the length of the sides of the triangle?
Mathematical reasoning & proof. Generalising. Isosceles triangles. Long problems. Quadratic equations. Creating expressions/formulae. Pythagoras' theorem. Simultaneous equations. Golden ratio. Making and proving conjectures.
Published June 1999.
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