SOLUTION: 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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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?
Answer by mananth(16946) About Me  (Show Source):
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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=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29

x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-90%2Bsqrt%2814884%29%29%2F8%29%29
x1= 4
x2= negative so ignore
walk width = 4 feet
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m.ananth@hotmail.ca