NRICH: 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?

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

2 by 3 rectangle

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

3 by 4 rectangle

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

4 by 6 rectangle

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?

Age 11 to 14


Algebra & Pre-Algebra, Patterning & Sequencing
Middle School, High School, Educator

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NRICH (University of Cambridge)

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