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Fence It

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

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 $24cm^2$?

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 $24$cm$^2$?
  • What is the smallest perimeter you can make, if the area is $24$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.

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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