SOLUTION: A small rectangular playground that is 10 feet by 14 feet is going to have a grass border of uniform width on all sides. If the area of the grass border is 145 square feet, how wid

Question 236457: A small rectangular playground that is 10 feet by 14 feet is going to have a grass border of uniform width on all sides. If the area of the grass border is 145 square feet, how wide is the border?
Answer by checkley77(12844) (Show Source): You can put this solution on YOUR website!
10*14=140 ft^2 is the playground area.
10 plus 2 times the border times 14 plus 2 times the border=140+145.
(10+2x)(14+2x)=140+145
140+28x+20x+4x^2=285
4x^2+48x+140-285=0
4x^2+48x-145=0

x=(-48+-sqrt[48^2-4*4*-145)/2*4
x=(-48+-sqrt[2,304+2,320)/8
x=(-48+-sqrt4,624)/8
x=(-48+-68)/8
x=(-48+68)/8
x=20/8
x=2.5 ft. is the width of the border.
Proof:
(10+2*2.5)(14+2*2.5)=285
(10+5)(14+5)=285
15*19=285
285=285
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