Test and analysis: (1) The base and height of the corresponding triangle can be expressed by similarity, so that the areas are equal;
(2) When the corresponding total investment is expressed by an algebraic expression containing X, the maximum value of quadratic function can be obtained.
Problem analysis: (1) Let FG=x meters, then AK = (80-x) meters.
From △AHG∽△ABC, BC= 120, AD=80, we can get: ∴HG=, Be+FC = 120 ∴ () =, ∴. When FG.
(2) Assume that the total investment after transformation is W yuan.
So W=
= ,
∵ Quadratic coefficient 6 > 0, 0 < x ≤ 80, ∴ When x=20, w is minimum = 26400.
Answer: When the side length FG of rectangular EFGH is 20m, the total investment of open space reconstruction is the smallest, with the minimum value of 26,400 yuan.