SOLUTION: Please help me with this word problem. A rectangular garden is to be surrounded by a walkway of constant width. The garden's dimensions are 30ft. by 40ft. The total area, gard

Question 110434: Please help me with this word problem.
A rectangular garden is to be surrounded by a walkway of constant width. The garden's dimensions are 30ft. by 40ft. The total area, garden plus walkway, is to be 1800 ft^2. What must be the width of the walkway to the nearest thousandth?

Thank you!
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
30*40=1200 sqft for the garden area.
adding the walk way we have an area is:
(30+2x)(40+2x)=1800
1200+80x+60x+4x^2=1800
4x^2+140x+1200-1800=0
4x^2+140x-600=0
4(x^2+35x-150)=0
using the quadratic equation we get:

x=(-35+-sqrt[35^2-4*1*-150)/2*1
x=(-35+-sqrt[1225+600])/2
x=(-35+-sqrt1825)/2
x=(-35+-42.72)/2
x=(-35+42.72)/2
x=7.72/2
x=3.86 answer for the width of the walkway.
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