Question 1151640
you have L = 3W
you have A = L * W
this becomes A = 3W * W = 3W^2
2/3 * A becomes 2/3 * 3W^2 = 2W^2
you are given that (L + 4) * (W - 2) = 2/3 * A
this makes (L + 4) * (W - 2) = 2W^2
since L = 3W, this becomes (3W + 4) * (W - 2) = 2W^2
simplify to get 3W^2 - 6W + 4W - 8 = 2W^2
combine like terms to get 3W^2 - 2W - 8 = 2W^2
subtract 2W^2 from both sides of this equation to get W^2 - 2W - 8 = 0
factor this quadratic equation to get (W + 2) * (W - 4) = 0
solve for W to get W = 4 or W = -2
W has to be positive, so W = 4
L = 3W, therefore L = 12


the original area is L * W = 12 * 4 = 48
the revised area is (L+4) * (W-2) = (12 + 4) * (4 - 2) = 16 * 2 = 32
the revised area divided by the original area is 32/48 = 2/3.


everything checks out so the solution looks good.
the solution is that the original width is 4 meters and the original area is 48 square meters.