The figure shows a right-angled triangle, LMN, drawn on a grid.
- LMP is a right-angled triangle with the same area as triangle LMN. Identify point P on the grid.
- LPQ is an equilateral triangle. Identify point Q on the grid such that it does not overlap with triangle LMN.
- Find the ratio of the area of triangle LMN to the area of triangle NPQ.