SOLUTION: A family plans to surrond their pool with a patio of constant width. The pool has an area of 150 square feet. The dimensions of the pool with the patio will be 15 feet by 20 feet.

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Question 37757: A family plans to surrond their pool with a patio of constant width. The pool has an area of 150 square feet. The dimensions of the pool with the patio will be 15 feet by 20 feet. Find the dimensions of the pool.
Answer by junior403(76) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the width of the patio.
From the problem...
(length of the total area - patio)*(width of the total area - patio) = area of pool 150.
Since the patio borders the entire area we need to account for it twice.
So, our equation is...
(20-2x)(15-2x)= 150
FOIL...
300 - 70x + 4x^2 = 150
Subtract 150 from both sides...
150 - 70x + 4x^2 = 0
In standard form this becomes...
4x^2 -70x +150 = 0
This can be simplified by factoring out a 2...
2(2x^2 - 35x + 75) = 0
Then factor completely...
(2x^2 - 30x) - (5x +75) = 0
And...
2x(x - 15) -5(x - 15) = 0
With the result...
(x-15)(2x-5) = 0
So...
(x-15) = 0 or (2x-5) = 0
x = 15 or x = 2.5
Since the width of the entire area is 15, the width of the patio cannot be 15 so that eliminates x = 15 as a correct result.
So the width of the patio is 2.5 feet.
To find the dimensions of the pool we subtract our answer from the total length and width. Substitute answer in original equation.
20 - 2(2.5) = 20 - 5 = 15
and...
15 - 2(2.5) = 15 - 5 = 10
and...
15 * 10 = 150 (the total area of the pool.
So...
The pool is 15' x 10'
I hope this helps
Good Luck!