SOLUTION: A garden measuring 12 meters by 16 meters is to have a pedestrain pathway installed all around it, increasing the total area to 285 meters. What will be the width of the pathway?

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Question 858993: A garden measuring 12 meters by 16 meters is to have a pedestrain pathway installed all around it, increasing the total area to 285 meters. What will be the width of the pathway?

Answer by mananth(16946) (Show Source):
You can put this solution on YOUR website!
Let the width of sidewalk be x
..
Length of garden 16 m
width of garden 12 m

Area = 192m^2
Area of sidewalk = 285-192= 93m^2
Area of sidewalk 93 m^2
length of garden & sidewalk 16 + 2 x
width of garden & sidewalk 12 + 2 x
Total area - area of garden = 93

( 16 + 2 x ) ( 12 + 2 x ) -192 = 93

192 + 32 x + 24 x + 4 X^2 -192 = 93
4 X^2 + 56 x -93 = 0
4x^2+56x = 93
/4
x^2+14x=93/4
completing the square method
x^2+14x+49=93/4 +49
(x+7)^2 = (196+93)/4
(x+7)^2= 289/4
take square root
(x+7) = +/- sqrt((289)/4)
(x+7) =+/- 17/2
x=17/2-7 Taking the positive value
x= 8.5-7
x=1.5 m the width of walkway