1.18: Perimeter and area inequalities for a rectangle

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

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

(i) $P$,

(ii) $A$.

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

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