1.2: Perimeter and area inequalities for a rectangle

Figure 2 shows a rectangle with width $\displaystyle x$ metres and length $\displaystyle (x+4)$ metres. Its perimeter is $\displaystyle P$ metres and its area is $\displaystyle A\,\mathrm{m}^2$.

(a) Find, in terms of $\displaystyle x$, an expression for

(i) $\displaystyle P$,

(ii) $\displaystyle A$.

The perimeter has to be less than $\displaystyle 30$ metres. The area has to be greater than $\displaystyle 12\,\mathrm{m}^2$.

(b) Find the set of possible values for $\displaystyle x$. Give your answer in the form