Line of Squares

Age 11 to 14

ShortChallenge Level Yellow star

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:

$4a+4b+4c+4d+4e+4f = 4\left(a+b+c+d+e+f\right) = 4 \times 24\text{cm} = 96\text{cm}$

This problem is taken from the UKMT Mathematical Challenges.

You can find more short problems, arranged by curriculum topic, in our short problems collection.

You may also like