Question 284608: Please help! A rectangular pool that is 20ft. long and 25ft. wide is to be surrounded by a concrete walk of uniform width. If the owner can only afford to pay for enough concrete to create a total walk area of 504 sq. ft., what is the width of this walk?
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! Please help! A rectangular pool that is 20ft. long and 25ft. wide is to be surrounded by a concrete walk of uniform width. If the owner can only afford to pay for enough concrete to create a total walk area of 504 sq. ft., what is the width of this walk?
let the width of the walk be x
The length of pool +walk will be 2x+25 ( width x on both sides of the pool)
The width will be 2x+20
The area of pool +walk = (2x+20) * (2x+25)
The area of the pool = 20*25
(2x+20)(2x+25)- 500= 504
2x(2x+25)+20(2x+25)-500=504
4x^2+50x+40x+500-500=504
4x^2+90x-504=0
2x^2+45x-252=0
a=2, b= 45 * c= -252
b^2-4ac= 4041
x1= -45+sqrt4041 / 2*2
=4.64
x2=-45-sqrt4041 / 2*2
x2=-27.1
the width of the walk = 4.64 feet
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