(i)[2]
Show that the area, $A\,\text{m}^2$, of the playground is given by $A = x^2 - 30x + 1200$.
(ii)[3]
As $x$ is allowed to change, determine the smallest possible area of the playground.
Mathematics 9709 · AS & A Level · Quadratics
Quadratics — practice question
A diagram gives a layout for a rectangular park $ABCD$, where $AB = 40\,\text{m}$ and $AD = 60\,\text{m}$. The points $X$ and $Y$ are located on $BC$ and $CD$ respectively, and the paths $AX$, $XY$ and $YA$ enclose a triangular playground. The distance $DY$ is $x\,\text{m}$, while $XC$ is $2x\,\text{m}$.