Question 398013
A rectangular plot of ground having dimensions 21 ft by 24 ft is surrounded by a walk of uniform width. If the area of the walk is 424 ft2, what is its width?
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area of ground = 21*24=504 ft^2
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area of walk = 424 ft^2
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let width of walk be x
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width of total area = 21+2x
length of total area = 24+2x
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Area of total area = (21+2x)(24+2x)
Total Area = 504+90x+4x^2
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4x^2+90x+504-504 = 424
4x^2+90x-424=0


Find the roots of the equation by quadratic formula
a= 4  , b =90   , c = -424    .

b^2-4ac=14884
{{{x=(-b+-sqrt(b^2-4ac))/(2a)}}}


{{{x1=(-b+sqrt(b^2-4ac))/(2a)}}}
{{{x1=(-90+sqrt(14884))/8))}}}
x1= 4
x2= negative so ignore

walk width = 4 feet
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