SOLUTION: A concrete border is constructed around a rectangular flower bed that is 12ft by 9ft. Find the width of the border if the total area formed by the flower bed and the border is 154f

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Question 1001377: A concrete border is constructed around a rectangular flower bed that is 12ft by 9ft. Find the width of the border if the total area formed by the flower bed and the border is 154ft^2.
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
Let the width of sidewalk be x
..
Length of garden = 12 m
Width = 9 m 315.64

Area = 108 m^2
Area of sidewalk = 46 m^2
Length of ground + sidewalk = 12 + 2 x
width of ground + sidewalk = 9 + 2 x

( 12 + 2 x ) ( 9 + 2 x ) + -108 = 46

108 + 24 x + 18 x + 4 X^2 + -108 = 46
4 X^2 + 42 x + -46 = 0
Find the roots of the equation by quadratic formula
a= 4 b= 42 c= -46
b^2-4ac= 1764 - -736
b^2-4ac= 2500 sqrt%28%092500%09%29= 50
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=( -42 + 50 )/ 8
x1= 1
x2=( -42 -50 ) / 8
x2= -15.5
Ignore negative value
width of sidewalk = 1 m