The diagram contains a small rectangle positioned inside a larger rectangle. The larger rectangle has height $x$ cm. Its length is $4$ times its height. The shaded border has width $3$ cm. The area of the small rectangle is $80\,\text{cm}^2$.
(a)[4]
Form an equation in $x$ and show that it reduces to $2x^2 - 15x - 22 = 0$.
(b)[3]
Find the solutions of $2x^2 - 15x - 22 = 0$. Show your working and give your answers correct to $2$ decimal places.
(c)[2]
Calculate the area of the shaded region.
Worked solution & mark scheme
This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: “The brackets are expanded accurately” …