SOLUTION: Dimensions of a Border Around a Pool A club swimming pool is 30 feet wide and 40 feet long. The club members want an exposed aggregate border in a strip of uniform width around

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Question 343844: Dimensions of a Border Around a Pool
A club swimming pool is 30 feet wide and 40 feet long. The club members want an exposed aggregate border in a strip of uniform width around the pool. They have enough material for 296 square feet. How wide can the strip be?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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Dimensions of a Border Around a Pool
A club swimming pool is 30 feet wide and 40 feet long.
The club members want an exposed aggregate border in a strip of uniform width around the pool.
They have enough material for 296 square feet.
How wide can the strip be?
:
Let x = the width of the border
then
(2x+30) by (2x + 40) are the overall dimensions of the pool and the border
:
use the area to find x:
Overall area - pool area = 296 sq/ft (aggregate area)
(2x+30)*(2x+40) - (30*40) = 296
FOIL
4x^2 + 80x + 60x + 1200 - 1200 = 296
:
Arrange as a quadratic equation
4x^2 + 140x + 1200 - 1200 - 296 = 0
4x^2 + 140x - 296 = 0
:
simplify, divide by 4, results:
x^2 + 35x - 74 = 0
:
Factor to
(x+37)(x-2) = 0
:
The positive solution is what we want here:
x = 2 ft is the width of the border around the pool
:
:
:
Check solution by finding the areas
(30+4)(40+4) - (30*40) =
(34 * 44) - 1200 =
1496 - 1200 = 296; confirms our solution of x = 2 ft