Squares in rectangles

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?
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Squares in Rectangles printable worksheet

 

A $2$ by $3$ rectangle contains $8$ squares. Can you see how?

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Squares in rectangles


A $3$ by $4$ rectangle contains $20$ squares. Can you see how?

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Squares in rectangles


A $4$ by $6$ rectangle contains $50$ squares. Can you see how?

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Squares in rectangles


What size rectangle contains exactly $100$ squares?

Is there more than one?

Can you find them all?

Can you prove that there are no more?

Click here for a poster of this problem.