Write down an expression for the area, \(A\), in \({{\text{m}}^2}\), of the carpet.

The area of the carpet is \({\text{10 }}{{\text{m}}^2}\).

Calculate the value of \(x\).

The area of the carpet is \({\text{10 }}{{\text{m}}^2}\).

Hence, write down the value of the length and of the width of the carpet, in metres.

\(2x(x - 4)\)   or   \(2{x^2} - 8x\)     (A1)     (C1)

Note: Award (A0) for \(x - 4 \times 2x\).

[1 mark]

\(2x(x - 4) = 10\)     (M1)

Note: Award (M1) for equating their answer in part (a) to \(10\).

\({x^2} - 4x - 5 = 0\)     (M1)

OR

Sketch of \(y = 2{x^2} - 8x\) and \(y = 10\)     (M1)

OR

Using GDC solver \(x = 5\) and \(x =  - 1\)     (M1)

OR

\(2(x + 1)(x - 5)\)     (M1)

\(x = 5{\text{ (m)}}\)     (A1)(ft)     (C3)

Notes: Follow through from their answer to part (a).

     Award at most (M1)(M1)(A0) if both \(5\) and \(-1\) are given as final answer.

     Final (A1)(ft) is awarded for choosing only the positive solution(s).

[3 marks]

\(2 \times 5 = 10{\text{ (m)}}\)     (A1)(ft)

\(5 - 4 = 1{\text{ (m)}}\)     (A1)(ft)     (C2)

Note: Follow through from their answer to part (b).

     Do not accept negative answers.

[2 marks]