Stage Four

Problem No. 4 Vegetable Garden

 

My vegetable garden is rectangular and is surrounded by a 1 metre path. The area of the garden is 36 m².

How many square metres of paved path might there be?

How many solutions are there?

How can you tell when you have them all?

If each paver is 1 m², what is the least number of pavers needed to build the path?

Hints:

1. Draw a diagram of the garden on 1 cm grid paper and add a 1 metre wide path

 2. Draw a table.

 

Number of metres in garden length
Number of metres in garden width
Number of metres in path length
Number of metres in path width
Total number of pavers needed

 All Stage 4 Problems

  No answers came in for this one, so I'll give it a go myself. First to draw some diagrams...

These are the only shapes that I can find that work - I think that is all there is.

Notice I've assumed that we are working in whole numbers. If you limit it to whole numbers, there are 5 possible garden layouts, as shown above.

Now to fill in the table...

 

Number of metres in garden length	6	9	12	18	36
Number of metres in garden width	6	4	3	2	1
Number of metres in path length	8	11	14	20	38
Number of metres in path width	8	6	5	4	3
Total number of pavers needed	28	30	34	44	78

Notice that the path length is always 2 metres longer than the length of the garden side. If you don't trust me on this, count out the squares!

The number of square metres of path (and hence the number of pavers) can be worked out easily (if slowly) by counting. Can you see a faster, mathematical way?

So a 6m by 6m garden needs the least (28) pavers.