# Rabbit Run

Ahmed wants to build an outdoor run for his rabbit.

He has decided that it will go against one wall of the shed.

Ahmed has some wooden planks to use for the other sides of the rabbit run. Some are 4m long, some 5m and some 6m.

If he uses three planks, he will be able to make the rabbit run in the shape of a quadrilateral.

What quadrilaterals would he be able to make if he uses three planks the same length?

Why?

What quadrilaterals would he be able to make if he uses two planks the same length and one a different length?

Why?

What quadrilaterals would he be able to make if he uses three planks which are all different lengths?

Using three identical sticks, can you make any quadrilaterals which have all four sides the same length?

Do all four sides have to be the same length?

Thank you to all those who sent solutions to Rabbit Run. Don't forget, even though we asked you to use planks of certain lengths, we didn't say that the length along the side of the shed had to be a particular length. Charles Price-Smith from L.I.S. and Henry from Wells Cathedral School sent in well thought out solutions - they both looked at all the possibilities.

Henry said that when you've got three planks the same length you can make a square, a trapezium and a rhombus. When two planks are the same, you can make a rectangle, parallelogram, trapezium and a kite.

Charles wrote:

If he uses all three logs of a different length he will only be able to make the shape of a trapezoid (another word for trapezium).

### Why do this problem?

This problem will challenge pupils' knowledge of the properties of quadrilaterals. It is a good context for 'proof by exhaustion'.

### Possible approach

It might be useful to have some plastic quadrilaterals available so that the children can refer to them during the task. Children should be encouraged to 'prove by exhaustion' that they have found all possible shapes.

### Possible extension

This problem could be extended into compiling minimum sets of criteria to distinguish different quadrilaterals from each other. For example:

a rhombus and a kite

a rhombus, a kite and a square

a rhombus, a kite, a square and a rectangle.