Question 328113: A small rectangular playground that is 10ft by 14ft is going to have a grass border of a uniform width on all sides. If the area of the grass border is 145 sqare feet, how wide is the border?
I have tried to think of the correct formula but have come up blank! please can someone help me with this one!
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A small rectangular playground that is 10ft by 14ft is going to have a grass
border of a uniform width on all sides.
If the area of the grass border is 145 square feet, how wide is the border?
:
Find the area of the playground: 10 * 14 = 140 sq/ft
:
Let x = the width of the border
:
Then the overall dimensions including the border will be: (2x+10) by (2x+14)
Find the overall area (A)
A = (2x+10)*(2x+14)
FOIL
A = 4x^2 + 28x + 20x + 140
A = 4x^2 + 48x + 140
:
Overall area - playground area = border area, therefore:
4x^2 + 48x + 140 - 140 = 145
Arrange as a quadratic equation
4x^2 + 48x - 145 = 0
You can use the quadratic formula here, but this will factor
(2x-5)(2x+29) = 0
The positive solution is what we want here
2x = 5
x = 5/2
x = 2.5 ft is the width of the grass border
:
:
Check our solution by finding the overall area and subtracting the playground area
(5+10)*(5+14) = 285 sq/ft
285 - 140 = 145 sq/ft; confirms our solution of x=2.5
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