SOLUTION: I have been trying to solve this word problem and could use someone's help(note that the chapter is on quadratic equations): A garden area is 30 ft long and 20 ft wide. A path of

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I have been trying to solve this word problem and could use someone's help(note that the chapter is on quadratic equations): A garden area is 30 ft long and 20 ft wide. A path of      Log On


   

Question 108339: I have been trying to solve this word problem and could use someone's help(note that the chapter is on quadratic equations):
A garden area is 30 ft long and 20 ft wide. A path of uniform width
is set around the edge. If the remaining garden area is 400 ft2, what is the width of the path?
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A garden area is 30 ft long and 20 ft wide. A path of uniform width
is set around the edge. If the remaining garden area is 400 ft2, what is the width of the path?
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Draw the figure of a rectangle surrounding a rectangle
The inner rectangle has area = 400 ft^2
The larger rectangle has area = 30*20 = 600 sq. ft.
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Let the width of the path be "x" ft.
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Then the inner rectangle has dimensions:
width = 30-2x
length = 20-2x
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EQUATION:
(30-2x)(20-2x)=400
(15-x)(10-x) = 100
150-25x+x^2 = 100
x^2-25x+50 = 0
x = [25 +- sqrt(25^2-4*40)]/2
x = [25 +- sqrt(425)]/2
x = [25 +- 5sqrt(17)]/2
Realistic answer:
x = [25-5sqrt(17)]/2
x = 2.1922.. ft.
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Cheers,
Stan H.