A rectangular park has an area of \(864\) \(m^2\). If its length is \(12\) \(m\) more than its width, a path of uniform width \(2\) \(m\) is built inside the garden along all four sides.
Find:
1. The original dimensions of the garden.
2. The area left for planting \(=\)______ \(m^2\)
3. The area of the path \(=\)_______ \(m^2\)