II got the correct answer but I have a question about Greg’s approach. In this question, Greg assumed that the area of each of the 4 smaller triangles within the rectangle is 1. Why did he assume this?

When there are 2 diagonals in a rectangle, it does not mean that the diagonals divide the rectangle into 4 equal triangles, right?

It is not assumption, it is something that you derive from this problem. Recall that the diagonals of a rectangle bisect each other, so triangle BOE and AOF are isosceles and equal, and triangles BOA and EOF are another pair of isosceles and equal triangles. Try deriving the relation that exists among the sides.