A farmer uses $160$m of fencing to enclose a plot of his land in a shape that comprises an isoscel

Question

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. Show that the area of the plot is $\frac{320\sqrt{3}x - (3\sqrt{3} + 6)x^2}{4} m^2$. Given that $x$ can vary, find the value of $x$ for which the area of the plot is stationary. 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.

Accepted Answer

$x = 24.8 m (3 s.f.), Maximum area = 1715 m²$

2017 PLMGS P1

2017 PLMGS P1

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