Year 7 Measurement Analysis Task

Name:______Form:______Due Date:______

Fencing in the Vegetable Patch

For a long time, Tom’s wife has complained that the farm animals get into her vegetable patch, trampling and eating the vegetables. Tom’s solution is to fence in the garden to keep the animals out. Looking in the shed, he discovers that he has a roll of fencing wire that is 40 meters long.

Being a practical man, Tom wants to make the best use of the fencing mesh and provide his wife with the largest garden possible. He is only prepared to make a rectangular fence, and the side dimensions must be whole numbers.

Question 1 (10 marks)

Draw diagrams on graph paper of all the rectangular shaped garden beds Tom can make with 40 meters of fencing (HINT: there are more than 9!)

Question 2 (10 marks)

Record your results of all the fencing possibilities in the table below. Work out the total area that is enclosed by the fencing in each case.

Length (m) / Width (m) / Perimeter (m) / Area (m2)

Question 3 (2 marks)

Which fencing option should Tom choose so that his wife will have the largest possible vegetable patch? (Don’t forget to include the unit of measure)

To provide an even larger area for his wife’s vegetable patch, Tom considers using the 16 metre wall of his large shed along one of the boundaries to the garden. He plans to investigate whether it is best used as a whole edge or as a part edge to the garden.

Question 4 (4 marks)

Using the 16 metre wall as an entire or partial edge to the garden and the 40 metres of fencing wire, investigate the possible rectangular fences that can be constructed to produce a larger vegetable patch for Tom’s wife.

Question 5 (2 marks)

Attach a drawn diagram on graph paper of your final design, showing:

a) the dimensions

b) how much of the shed’s wall is used

Question 6 (2 marks)

How do your findings from Question 3 differ from your results stated in Question 5?

Did the shed wall provide a larger area for the vegetable patch?