11 A lawn is to be made in the shape shown below. The units are metres.
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- The perimeter of the lawn is \(P \mathrm {~m}\). Find \(P\) in terms of \(x\).
- Show that the area, \(A \mathrm {~m} ^ { 2 }\), of the lawn is given by \(A = 9 x ^ { 2 } + 6 x\).
The perimeter of the lawn must be at least 39 m and the area of the lawn must be less than \(99 \mathrm {~m} ^ { 2 }\).
- By writing down and solving appropriate inequalities, determine the set of possible values of \(x\).