Question 1151640: `The length of a rectangle is three times it’s breadth .If the breadth is decreased by by 2m and the length increased by 4m,the area of rectangle is decreased by athird .Find the breadth of original rectangle.Hence finds its area.''.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 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.
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