1.1: Areas in a flag design

Figure 1 shows the design for a flag consisting of a white cross on a grey background. $\displaystyle AEFG$ and $\displaystyle DLMN$ are squares with sides of length $\displaystyle 3x\,\mathrm{cm}$. $\displaystyle BPQR$ and $\displaystyle CTUV$ are rectangles with sides of length $\displaystyle 5x\,\mathrm{cm}$ and $\displaystyle 3x\,\mathrm{cm}$. The width of the cross is $\displaystyle y\,\mathrm{cm}$.

The total area of the flag is $\displaystyle H\,\mathrm{cm}^2$.

(a) Write down an expression, in terms of $\displaystyle x$ and $\displaystyle y$, for $\displaystyle H$.

Given that the area of the cross is $\displaystyle K\,\mathrm{cm}^2$,

(b) show that

The total area of the flag is to be $\displaystyle 3432\,\mathrm{cm}^2$ and the area of the cross is to be $\displaystyle 1080\,\mathrm{cm}^2$.

(c) Find the value of $\displaystyle x$ and the value of $\displaystyle y$.