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# Perimeter Possibilities

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Age 11 to 14

Challenge Level

*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.