∫△EMN∽△EFA
∴AF AE =MN NE and ∵ Mn = AD-X =12-X.
NE=y-(AB-AE)=y-6
AF=4,AE=2
4 ^ 2 = 12-x y-6,
S=xy=70
Solution: x= 10, y=7.
Answer: The length and width of the rectangular MGCH are 10 decimeter and 7 decimeter respectively.
(2) Let the length of EM be a, △EMN∽△EFA, EM EF =MN AF =NE AE,
EF=2 5,MN=2 5 5 a,NE= 5 5 a,
MH=AD-MN= 12-2 5 5 a,MG=BE+EN=AB-AE+EN=6+ 5 5 a
∴S=MH×MG
=( 12-2 5 5 a)×( 6+ 5 5 a)
=-2 5 a2+72
Therefore, when a=0, the area is the largest, that is, point M and point E coincide.
At this time, the circumference L=2MH+2MG=36 decimeters.
Answer: When EM is 0, the area of the rectangular MGCH is the largest, and the circumference of the rectangle is 36 decimeters.