A rectangular picture $ABCD$ sits within a rectangular frame. Its length $AB$ is three times the height $x\,\text{cm}$. The frame has width $2\,\text{cm}$.
(a)[4]
The combined area of the picture and the frame is $476\,\text{cm}^2$. Form an equation in $x$ and show that it reduces to $3x^2+16x-460=0$.
(b)[3]
Solve the equation $3x^2+16x-460=0$ for $x$.
(c)[2]
Find the frame's height and length.
(d)[3]
The frame is constructed from wood. Its thickness is $5\text{ mm}$. The mass of $1\text{ cm}^3$ of the wood is $0.7\text{ g}$. Calculate the mass of wood used in the frame.
Worked solution & mark scheme
This 12-mark question has a full step-by-step worked solution and mark scheme. One marking point: “Expand the product $(x+4)(3x+4)$.” …