OCR Pure 1 2018 December — Question 2

Exam BoardOCR
ModulePure 1 (Pure Mathematics 1)
Year2018
SessionDecember
TopicInequalities

2
\includegraphics[max width=\textwidth, alt={}, center]{a16ab26f-21fb-4a73-8b94-c16bef611bcb-4_661_579_831_246} The diagram shows a patio. The perimeter of the patio has to be less than 44 m .
The area of the patio has to be at least \(45 \mathrm {~m} ^ { 2 }\).
  1. Write down, in terms of \(x\), an inequality satisfied by
    1. the perimeter of the patio,
    2. the area of the patio.
  2. Hence determine the set of possible values of \(x\).