Line of Squares
Weekly Problem 35 - 2016
What is the total perimeter of the squares, if the line GH in the diagram is 24cm?
What is the total perimeter of the squares, if the line GH in the diagram is 24cm?
Age
11 to 14
Challenge level
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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.
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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:
$4a+4b+4c+4d+4e+4f = 4\left(a+b+c+d+e+f\right) = 4 \times 24\text{cm} = 96\text{cm}$