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Laura Turner and Laura Malarkey from the Mount School have explained how they worked out the answer to this problem:
n is equal to the number of tiles along one side.
We can calculate the number of edges in two different ways:
Method 1 - In total there are n ² tiles on
4n ² edges.
Method 2 - There are a total of 2n green edges which implies
there are a total of 20n edges of all colours.
Therefore:
20n = 4n ²
5n = n ² (divide by 4)
5 = n (divide by n)
So there are 25 tiles in the set.
Can you work out the area of the inner square and give an explanation of how you did it?
With one cut a piece of card 16 cm by 9 cm can be made into two pieces which can be rearranged to form a square 12 cm by 12 cm. Explain how this can be done.