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

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Question 57969: 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 ankor@dixie-net.com(22740) (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 x = length of the original pool
Original pool dimensions:
x by (x-2)
Original pool:
area = x * (x-2)
original area = x^2-2x
:
New pool dimensions
(x + 4) by (x-2)-3)
(x+4) by (x-5)
New Area = (x+4)(x-5) = x^2 - x - 20
:
It said the areas would be the same so we can say:
x^2 - 2x = x^2 - x - 20
:
x^2 - x^2 - 2x + x = - 20
-1x = -20
x = -20/-1
x = +20
:
The original pool dimensions: 20 by 18.
:
Check using the areas
Old pool: 20 * 18 = 360 sq ft
New pool: 24 * 15 = 360 also