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?

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

2 by 3 rectangle

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

3 by 4 rectangle

A 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

STEAM Topics Resource Audience Grade Level Tags PDFs

Math Topics

Algebra & Pre-Algebra, Patterning & Sequencing

Middle School, High School, Educator

6th Grade, 7th Grade, 8th Grade, 9th Grade

Math Puzzles, Parallelograms

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