Perimeter Possibilities

I'm thinking of a rectangle with an area of 24. What could its perimeter be?
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Problem

Perimeter Possibilities printable sheet

 

Watch the video below.



How many other possible perimeters can you find, for a rectangle with an area of $24\text{cm}^2$?

Now watch the video to see what Alison and Charlie did next.



Here are some questions you might like to consider:

  • What other odd number perimeters can you make, if the area is $24\text{cm}^2$?
  • What is the smallest perimeter you can make, if the area is $24\text{cm}^2$?
  • What about the largest perimeter?
  • Which perimeters in between is it possible to make?



More generally...

  • Is it possible to make a rectangle with a fractional perimeter but a whole number area?
  • Is it possible to make a rectangle with a whole number perimeter but a fractional area?



Take a look at Can They Be Equal? to explore rectangles where the area is numerically equal to the perimeter.