Area of a path around a lawn

A rectangular lawn measures \(12\text{ m}\) by \(8\text{ m}\). It is surrounded by a path of uniform width \(x\text{ m}\).

1. Show that the area of the path is \((4x^2+40x)\text{ m}^2\).[2]
2. The path is paved with tiles costing \(\$25\) per \(\text{m}^2\). Find the cost of paving the path when \(x=1.5\).[2]
3. The owner says that doubling the width of the path will double its area. Use your expression from part (a) to explain whether she is correct.[2]
4. State one assumption about the path that was used in part (a).[1]