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# Perimeter Possibilities

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### Framed

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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.

Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of the pictures.

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

The diagram shows a large rectangle composed of 9 smaller rectangles. If each of these rectangles has integer sides, what could the area of the large rectangle be?