A creative landscaper wants to lay concrete kerb stones around the perimeter for his flowerbeds as s

Question

A creative landscaper wants to lay concrete kerb stones around the perimeter for his flowerbeds as shown in the diagram below. The flowerbed is made up of a rectangle $PQRS$ with a semicircle on the outer side of $PS$ and a quadrant of a circle on the outer side of $QR$. The length of $PS$ is $2x$ m and the length of $PQ$ is $y$ m. The total perimeter of the flowerbed is $50$ m. Show that the area, $A$ $\mathrm{m}^2$, of the flowerbed is given by $$A = 50x - \frac{1}{2}(4 + \pi)x^2.$$[3] The landscaper would like to maximise the area of the flowerbed. Use a non-calculator method to find the exact maximum value of $A$. You do not need to justify that this is a maximum value.[3]

Accepted Answer

(b) Maximum value of A = $\frac{1250}{4+\pi}$

2024 VJC H1 Q2

2024 VJC H1 Q2