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?
Age
11 to 14
Challenge level
Problem
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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.
Student Solutions
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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 $5\text{cm} \times 20 = 100\text{cm} = 1\text{m}$.