Mathematics 4024 · O Level · Equations

Equations — practice question

The diagram represents a cuboid. Its length is $x$ cm. Its height is $3$ times its length. Its width is $4$ cm less than its length.
(a)[2]

Write down expressions, in terms of $x$, for the cuboid's height and width.

(b)[4]

Given that the cuboid has surface area $200\text{ cm}^2$, form an equation in $x$ and demonstrate that it reduces to $7x^2 - 16x - 100 = 0$.

(c)[3]

Solve the equation $7x^2 - 16x - 100 = 0$. Give your answers accurate to $2$ decimal places.

(d)[1]

Find the cuboid's height.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: height is given by $3x$

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