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 283675: 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? Show all steps necessary to arrive at your solution. Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website! 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? Show all steps necessary to arrive at your solution.
Let the width of the grass border be x
The width of the total plot will be 10+2x ( x on each side of the playground)
The length of the plot will be 14+2x
Area of the total plot - area of the playground = AREA OF THE GRASS BORDER
(2x+10)(2x+14)-10*14= 145
4x^2+28x+20x+140-140=145
4x^2+48x-145=0
4x^2+58x-10x-145=0
4x(x+14.5)-10(x+14.5)=0
(x+14.5)(4x-10)=0
4x-10=0
4x=10
x=2.5 feet which is the width of the grass border
