Question 177390: The YMCA has a 40ft by 60ft area in which to build a swimming pool. The pool will have a sidewalk of uniform width around 3 sides. (The director of the YMCA does not want a sidewalk along one of the long sides of the pool) Let "x" be the width of the sidewalk.
A.) write a quadratic function in terms of "x" expressing the area of the pool
B.) The YMCA would like to construct the pool so that the area of the pool is at least half of the total area set aside for this project. Then state a reasonable interval for "x" that would satisfy this condition
Thank U!
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! The YMCA has a 40ft by 60ft area in which to build a swimming pool. The pool will have a sidewalk of uniform width around 3 sides. (The director of the YMCA does not want a sidewalk along one of the long sides of the pool) Let "x" be the width of the sidewalk.
:
A.) write a quadratic function in terms of "x" expressing the area of the pool
:
draw a rough diagram if this, one rectangle inside another, showing the walkway
on just 3 sides, a width of x. it will be apparent that the pool dimensions will be:
:
(60-2x) by (40-x), FOIL this and you have: 2400 - 60x - 80x + 2x^2, which is:
:
A(x) = 2x^2 - 140x + 2400; area of the pool
:
:
B.) The YMCA would like to construct the pool so that the area of the pool is at least half of the total area set aside for this project. Then state a reasonable interval for "x" that would satisfy this condition
:
Half of the total area = 1200 sq/ft; find the dimensions for this
pool area = 1200
2x^2 - 140x + 2400 = 1200
2x^2 - 140x + 2400 - 1200 = 0
2x^2 - 140x + 1200 = 0
simplify divide by 2;
x^2 - 70x + 600 = 0
Factor
(x-60)(x-10) = 0
two solutions
x = 60
and
x = 10 ft, the only solution that makes sense
We can say the walkway has to be 10 ft wide or less to ensure at least a 1200sq/ft pool
:
:
Check area if walkway is 10' wide:
(60-20) * (40-10) = 1200sq/ft
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