Poster with an exact length-to-width ratio

A rectangular poster has width \(w\) m and length \((2+\sqrt{3})w\) m. Its area is exactly \(2\) m\(^2\). Do not use a calculator in parts (a) and (b).

1. Show that \(w^2=4-2\sqrt{3}\).[2]
2. Hence show that \(w=\sqrt{3}-1\), and find the length of the poster in the form \(a+b\sqrt{3}\), where \(a\) and \(b\) are integers.[3]
3. A frame is made from one strip of moulding \(7\) m long. Each of the four corner joints wastes \(2\) cm of moulding. Determine whether one strip is enough to frame the poster, showing your reasoning.[3]