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Perimeter Possibilities

Stage: 3 Challenge Level: Challenge Level:1
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.