Question 985024
L=original length=12 meters; W=original width=8 meters; X=increase in size
Original Area=LW=(12m)(8m)=96m^2
New area =2(Original Area)=2(96m^2)=192m^2
.
(L+X)(W+X)=192m^2
(12m+X)(8m+X)=192M^2
X^2+20X+96=192
x^2+20X-96=0
(x+24)(x-4)=0
x+24=0 or x-4=0
x=-24m or x=4m 
Since x=-24m doesn't make sense, 
x=4 meters is the increase in lenght and width.
.
CHECK:
(L+X)(W+X)=2LW
(12m+4m)(8m+4m)=2(12m)(8m)
(16m)(12m)=2(96m^2)
192m^2=192m^2