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Paving the Way

A man paved a square courtyard and then decided that it was too small. He took up the tiles, bought 100 more and used them to pave another square courtyard. How many tiles did he use altogether?

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Square Areas

Can you work out the area of the inner square and give an explanation of how you did it?

Coloured Edges

Stage: 3 Challenge Level: Challenge Level:1

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 $n²$ tiles on $4n²$ edges.

Method 2 - There are a total of $2n$ green edges which implies there are a total of $20n$ edges of all colours.

Therefore:

$20n = 4n²$

$5n = n²$ (divide by $4$)

$5 = n$ (divide by $n$)

So there are $25$ tiles in the set.