6. The diagram shows a square divided into strips of equal width. Three strips are black and two are grey.
What fraction of the perimeter of the square is grey?
A $\frac{1}{5}$
B $\frac{1}{4}$
C $\frac{4}{25}$
D $\frac{1}{3}$
E $\frac{2}{5}$
Solution
A Two sides of the square are wholly black, and $\frac{2}{5}$ of two sides are grey. So the length of the perimeter that is grey is equal to $2 \times \frac{2}{5}=\frac{4}{5}$ of the length of one side. The length of the perimeter is 4 times the length of one side. So the fraction of the perimeter that is grey is
$$
\frac{\frac{4}{5}}{4}=\frac{1}{5} \text {. }
$$