SOLUTION: A rectangular swimming pool is 2 m longer than it is wide. If the width is decreased by 3 m, and the length is increased by 4 m, the area remains the same as the original area, Fin

Algebra ->  Rectangles -> SOLUTION: A rectangular swimming pool is 2 m longer than it is wide. If the width is decreased by 3 m, and the length is increased by 4 m, the area remains the same as the original area, Fin      Log On


   

Question 201130: A rectangular swimming pool is 2 m longer than it is wide. If the width is decreased by 3 m, and the length is increased by 4 m, the area remains the same as the original area, Find the original dimensions of the pool.
Answer by nerdybill(7384) About Me  (Show Source):
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A rectangular swimming pool is 2 m longer than it is wide. If the width is decreased by 3 m, and the length is increased by 4 m, the area remains the same as the original area, Find the original dimensions of the pool.
.
Let w = width of pool
then
w+2 = length of pool
.
(w-3)(w+2 +4) = w(w+2)
(w-3)(w+6) = w(w+2)
w^2+6w-3w-19 = w^2+2w
w^2+3w-19 = w^2+2w
3w-19 = 2w
w-19 = 0
w = 19 m (width of pool)
.
Length:
w+2 = 19+2 = 21 m (length of pool)
.
Dimensions: 19m x 21m