2017 PLMGS P1

A farmer uses \(160\)m of fencing to enclose a plot of his land in a shape that comprises an isosceles triangle and a rectangle, with the dimensions shown.

1. Show that the area of the plot is \(\frac{320\sqrt{3}x - (3\sqrt{3} + 6)x^2}{4} m^2\).
2. Given that \(x\) can vary, find the value of \(x\) for which the area of the plot is stationary.
3. Explain why this value of \(x\) gives the farmer the largest possible area for the plot. Find this area and give your answer correct to the nearest square metre.