Can they be equal?

Can you find rectangles where the value of the area is the same as the value of the perimeter?
Exploring and noticing Working systematically Conjecturing and generalising Visualising and representing Reasoning, convincing and proving
Being curious Being resourceful Being resilient Being collaborative

Can They be Equal? printable sheet



Charlie has been drawing rectangles:

 

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Can they be equal?
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Can they be equal?


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.