Edexcel C1 2014 June — Question 6

Exam BoardEdexcel
ModuleC1 (Core Mathematics 1)
Year2014
SessionJune
TopicInequalities

6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{6db8acbd-7f61-46ff-8fdc-f0f4a8363aa6-08_917_1322_239_303} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows the plan of a garden. The marked angles are right angles.
The six edges are straight lines.
The lengths shown in the diagram are given in metres.
Given that the perimeter of the garden is greater than 40 m ,
  1. show that \(x > 1.7\) Given that the area of the garden is less than \(120 \mathrm {~m} ^ { 2 }\),
  2. form and solve a quadratic inequality in \(x\).
  3. Hence state the range of the possible values of \(x\).