SOLUTION: Solve the following equations. Construction.A garden area is 30ft long and 20ft wide. A path of uniform width is set around the edge. If the remaining garden is 400ft^2, what is th
Question 75087This question is from textbook Beginning Algebra
: Solve the following equations. Construction.A garden area is 30ft long and 20ft wide. A path of uniform width is set around the edge. If the remaining garden is 400ft^2, what is the width of the path?
I am needing some help with this one. Thanks This question is from textbook Beginning Algebra
You can put this solution on YOUR website! Solve the following equations. Construction.A garden area is 30 ft long and 20ft wide. A path of uniform width is set around the edge. If the remaining garden is 400ft^2, what is the width of the path?
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Draw a diagrams of the this. Label the original area as 30 by 20. Label
the path width inside this area as x. Remaining garden is given as 400 sq ft
and it's dimensions are (30-2x) by (20-2x)
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The equation:
garden area = 400
(30-2x)*(20-2x) = 400
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FOILed
600 - 100x + 4x^2 = 400
:
4x^2 - 100x + 600 - 400 = 0
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A quadratic equation
4x^2 - 100x + 200 = 0
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Simplify divide by 4:
x^2 - 25x + 50 = 0
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Will not factor, use the quadratic formula: a=1, b=-25, c=+50
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x = 22.8, obviously this is not a solution
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x = 2.2 ft, is the width of the path
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Check to see of the dimensions of the garden give us an area of 400 sq ft
(30-4.4)(20-4.4) =
25.6 * 15.6 = 399.36 ~ 400
