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?
Investigate how this pattern of squares continues. You could
measure lengths, areas and angles.
Can you work out the area of the inner square and give an
explanation of how you did it?
Charlie has been drawing rectangles:
The first rectangle has a perimeter of 30 units and an area of 50 square units.
The second rectangle has a perimeter of 24 units and an area of 20 square units.
Charlie wondered if he could find a rectangle, with a side of length 10 units, whose perimeter and area have the same numerical value.
Can you find a rectangle that satisfies this condition?
Alison says "There must be lots of rectangles whose perimeter and area have the same numerical value."
Charlie is not so sure.
Can you find more examples of such rectangles?
Can you come up with a convincing argument to help Charlie and Alison decide who is right?
Click here for a poster of this problem.