Six Circles
In the diagram, six circles of equal size touch adjacent circles and the sides of the large rectangle. What is the perimeter of the large rectangle?
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![Six Circles Six Circles](/sites/default/files/styles/large/public/thumbnails/content-id-11654-Weekly%2525202016%252520-%25252033%252520Diagram.png?itok=Ergc9-j3)
Each of the corners of the small rectangle is the centre of one of the large circles.
The perimeter of the small rectangle is $60\text{cm}$.
What is the perimeter of the large rectangle?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Image
![Six Circles Six Circles](/sites/default/files/styles/large/public/thumbnails/content-id-11654-Weekly%2525202016%252520-%25252033%252520Solution.png?itok=HdaZmR6g)
Since this has a total length of $60\text{cm}$, each radius is of length $60\text{cm} \div 12 = 5\text{cm}$.
The large rectangle can also be broken down into segments of this length. These are shown in blue and red on the diagram. There are $20$ of these, so the perimeter of the large rectangle is $5\text{cm} \times 20 = 100\text{cm} = 1\text{m}$.