You may also like

problem icon

Pebbles

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

problem icon

Great Squares

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.

problem icon

Square Areas

Can you work out the area of the inner square and give an explanation of how you did it?

Carpet Cuts

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Katherine from Maidstone Girls Grammar School made very good use of the Excel spreadsheet software to draw her solutions. .

To find the ten by ten foot carpet from a twelve by nine foot carpet with an eight by one foot hole exactly in the middle, I started by making a lot of grids (9 by 12 with an 8 by 1 foot hole hole exactly in the middle) so that I would be able to try different ways to make it a 10 by 10 foot carpet.

At first, I was cutting in straight lines trying to make them fit. Just out of interest, I counted the squares in the carpet, there were 100. This meant that I couldn't overlap the carpet in any way.

From this information, I thought that it would only be possible by cutting diagonally, so I started to cut going up then across one at a time, then I worked it out like this.

RESULT. I found the solution, but there were two. A left and a right handed solution, here they are.

12 by 9 foot carpet diagram