Question 70083
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? 
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A rough drawing will aid in understanding this: 
Label the garden rectangle as 30 by 40 
Label the width of the walk-way as x, 
It should be apparent, that the outside dimensions, which include the walk-way, 
are (30+2x) by (40+2x):
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Area of the whole thing is given as 1800 sq ft, so we have:
(30+2x)*(40+2x) = 1800
:
1200 + 60x + 80x + 4x^2 = 1800;  FOILed (30+2x)(40+2x)
:
1200 + 140x + 4x^2 - 1800 = 0;
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4x^2 + 140x - 600 = 0; our old friend, the quadratic equation
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Simplify, divide equation by 4 and you have:
x^2 + 35x - 150 = 0

Does not easily factor, so use the quadratic formula:
a = 1; b = 35; c = -150
:
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
:
{{{x = (-35 +- sqrt( 35^2 - 4 * 1 * -150 ))/(2*1) }}}
:
{{{x = (-35 +- sqrt( 1225 - (-600) ))/(2) }}}
:
{{{x = (-35 +- sqrt( 1825 ))/(2) }}}
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We are only interested in the positive solution here
{{{x = ((-35 + 42.72))/2}}}
:
{{{x = (7.72)/2}}}
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x = 3.860 ft is the width of the path 
:
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Check our solution; add 2 * 3.86 to the given dimensions; 30 by 40
37.72 * 47.72 = 1799.9984 ~ 1800
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How about this? Did it make sense to you?