【Haichuan Teahouse】Another brain-teasing question
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As shown in the figure, there is a rectangle EFGH inside square ABCD. Point F is exactly the midpoint of BC, while points E and G lie on AB and AD respectively. Given that EF = 4, find the length of FG. You can guess what the area of this square is
There is no single answer; the area of the square lies within a certain range, with the side length not exceeding 8.
FG is 8. Draw a perpendicular from G to BC, intersecting it at point H. ΔGFH is similar to ΔFED. F is the midpoint, and GH = DC = BC; therefore, FG = 8
It is not unique to guess the area of the square; FG=8 is correct.
The limit substitution method can be used to find it
Points E and G restrict the conditions on AB and AD respectively. It’s not on the extension line
What does \"extreme\" mean? Do AB and EH overlap?