Math CentralQuandaries & Queries


Question from Maria, a parent:

Given a six by six square, how rectangles are there in the square?

Hi Maria.

A rectangle will have four sides: two vertical and two horizontal.

There are 6 "spaces", so there are 5 lines between them plus a line on each edge. So there are seven possible vertical lines and seven possible horizontal lines.


This means we need to find the number of ways of choosing 2 vertical lines from a group of seven and multiply that by the number of ways of choosing 2 horizontal lines from a group of seven to find the answer.

This can be written in two common forms:


Can you take it from here?

Stephen La Rocque.

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