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

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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) About Me  (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+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
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