Challenge Level

*Can They be Equal? printable sheet*

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 if Alison is right?**

Click here for a poster of this problem.