SOLUTION: A garden area is 30ft long and 20 ft wide. A path of uniform width is set around the edge. If the remaining garden area is 400ft^2, what is the width of the path?
No clue how to
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Question 89417This question is from textbook Beginning Al
: A garden area is 30ft long and 20 ft wide. A path of uniform width is set around the edge. If the remaining garden area is 400ft^2, what is the width of the path?
No clue how to even come up with equation - please help!
This question is from textbook Beginning Al
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A garden area is 30ft long and 20 ft wide. A path of uniform width is set around the edge. If the remaining garden area is 400ft^2, what is the width of the path?
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Draw a rectangle inside a rectangle.
The area in the outer rectangle but outside the inner rectangle is the path.
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Let the uniform width of the path be "x"
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Dimensions of the outer rectangle: 30 x 20
Area of outer rectangle = 600 sq ft
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Dimensions of the innner rectangle: (30-2x)(20-2x) = 4(15-x)(10-x)
= 4[150-25x+x^2] sq ft
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EQUATION:
4[150-25x+x^2] = 400
x^2-25x+150 = 100
x^2-25x+50= 0
x = [25+-sqrt(625-4*50)]/2
x = [25+-sqrt(425)]/2
x = [25+-5sqrt17]/2
x = [25+5sqrt17]/2 or x=[25-5sqrt1]/2
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Cheers,
Stan H.
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