SOLUTION: A 60 by 80-foot rectangular walk in a park is surrounds a flower bed. If the walk is of uniform width and its area is equal to the area of the flower bed, how wide is the walk.?

Question 103961: A 60 by 80-foot rectangular walk in a park is surrounds a flower bed. If the walk is of uniform width and its area is equal to the area of the flower bed, how wide is the walk.?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A 60 by 80-foot rectangular walk in a park is surrounds a flower bed. If the walk is of uniform width and its area is equal to the area of the flower bed, how wide is the walk.?
:
Total area: 60 * 80 = 4800
Since the walk and the flower bed have equal area,
Flower bed area = 2400 sq ft
:
Let sidewalk width = x
:
Dimension of the flower bed: (60-2x) by (80-2x)
Therefore:
(60-2x) * (80-2x) = 2400
:
4800 - 280x + 4x^2 = 2400; FOILed
:
4x^2 - 280x + 4800 - 2400 = 0
:
4x^2 - 280x + 2400 = 0; a quadratic equation
:
Simplify, divide by 4:
x^2 - 70x + 600 = 0
:
Factors to:
(x-60)(x-10) = 0
:
x = 10 ft is the width of the sidewalk (reasonable solution)
:
:
Check solution by finding out if the area is 2400
:
(60-20)*(80-20) = 2400 sq/ft
:
:
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