Six circular discs are packed in different-shaped boxes so that the
discs touch their neighbours and the sides of the box. Can you put
the boxes in order according to the areas of their bases?
Stage: 4 Challenge Level:
Why do this problem?
The first part is an easy application of the cosine rule. The
second part requires some algebraic skills and gives practice in
proving a formula.
Use as practice. The problem does not require learners to decide on
the method to use.
Look at the formula to be proved. Write down the cosine formula for
the triangles in the diagram using the same notation. Can you see
how to manipulate the formulas you have established to give the
formula to be proved?
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.