perimeter = 2length(L) + 2width( W) = 12ft
P = 2L + 2W
12 = 2L + 2W .........(1)
Area = length(L) x width(W) = 8 square feet
8 = L X W.........(2)
From 2 ...... W = 8/L
Substituting for W in (1) yields
12 = 2L + 2(8/L)
12 = 2L + 16/L
12L = 2L^2 + 16
Rearranging the equation yields
2L^2 -12L +16 = 0
L^2 - 6L + 8 =0
L^2 -4L - 2L +8 =0
(L^2 - 4L)(-2L + 8) = 0
L( L - 4) -2(L -4) = 0
(L-2)(L-4) = 0
L= 2ft
or
L = 4ft
If L = 2cm
from (2) , W = 8/L = 8/2 = 4ft
If L =4ft
from (2), W = 8/L = 8/4 = 2ft
L = 2ft when W = 4=ft OR L=4ft, when W= 2ft