A farmer splits a rectangular plot of land into $8$ equal rectangular sheep pens, as the diagram shows. Each pen has dimensions $x$ m by $y$ m and is completely surrounded by metal fencing. Altogether, the farmer uses $480$ m of fencing.
(i)[3]
Show that the land area occupied by the sheep pens, $A$ $\text{m}^2$, can be written as $A = 384x - 9.6x^2$.
(ii)[3]
Given that $x$ and $y$ may change, find the dimensions of each sheep pen for which $A$ is at its greatest value. (There is no need to check that $A$ is a maximum.)
Worked solution & mark scheme
This 6-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Form the area expression $A=2y\times 4x$.” …