SOLUTION: A 6 m by 9 m swimming pool is surrounded by a deck which has a constant width. How wide is the deck if its area equals the area of the pool?

Question 1007843: A 6 m by 9 m swimming pool is surrounded by a deck which has a constant width. How wide is the deck if its area equals the area of the pool?
Answer by fractalier(6550) (Show Source): You can put this solution on YOUR website!
If the deck has a width of x, then the dimensions of the pool and decking are 6+2x by 9+2x. Multiplying the original dimensions gives 54 m^2. Thus the area of the pool and decking are twice that, and we have
(6+2x)(9+2x) = 108
4x^2 + 30x + 54 = 108
4x^2 + 30x - 54 = 0
2x^2 + 15x - 27 = 0
(2x - 3)(x + 9) = 0
so that the deck width x has to be
x = 3/2 = 1.5 m
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