Line of Squares
Weekly Problem 35 - 2016
What is the total perimeter of the squares, if the line GH in the diagram is 24cm?
Problem
In the diagram on the right, each of the squares touches adjacent squares at the corners and the line $GH$ along one of the edges.
If the length of $GH$ is $24\text{cm}$, what is the total perimeter of all the squares?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Each square has exactly $\frac{1}{4}$ of its perimeter as part of the line, and together these form the whole line. This means the total perimeter is $4 \times 24\text{cm} = 96\text{cm}$.
Algebraically, the diagram on the left shows that the line has length $a+b+c+d+e+f = 24\text{cm}$. The total of the perimeters is then: