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?

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Age 11 to 14

Math Topics
Algebra & Pre-Algebra, Patterning & Sequencing
Middle School, High School, Educator
6th Grade, 7th Grade, 8th Grade, 9th Grade
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Click here for a poster of this problem.

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NRICH (University of Cambridge)

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