The diagram depicts a metal plate made up of a rectangle with side lengths $x\,\text{cm}$ and $y\,\text{cm}$ together with a quarter-circle of radius $x\,\text{cm}$. Its perimeter measures $60\,\text{cm}$. Since $x$ may vary,
(a)[2]
Write $y$ in terms of $x$.
(b)[2]
Show that the area of the plate, $A\,\text{cm}^2$, can be written as $A = 30x - x^2$.
(c)[2]
Find the value of $x$ for which $A$ is stationary.
(d)[2]
Find this stationary value of $A$, and decide whether it is a maximum or a minimum value.
Worked solution & mark scheme
This 8-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Apply perimeter equation $2x+2y+\frac{\pi x}{2}=60$” …