SOLUTION: A garden measuring 12 by 24 meters is to have a sidewalk installed all around it, increasing the total area to 423.64 square meters. What will be the width of the pathway?

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Question 729258: A garden measuring 12 by 24 meters is to have a sidewalk installed all around it, increasing the total area to 423.64 square meters. What will be the width of the pathway?
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 = 24 m
Width = 12 m Total area - area of garden =135.64

Area = 288 m^2
Area of sidewalk = 135.64 m^2
Length of ground + sidewalk = 24 + 2 x
width of ground + sidewalk = 12 + 2 x

( 24 + 2 x ) ( 12 + 2 x ) + -288 = 135.64

288 + 48 x + 24 x + 4 X^2 + -288 = 135.64
4 X^2 + 72 x + -135.64 = 0
Find the roots of the equation by quadratic formula
a= 4 b= 72 c= -135.64
b^2-4ac= 5184 - -2170.24
b^2-4ac= 7354.24 sqrt%28%097354.24%09%29= 85.76
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=( -72 + 85.76 )/ 8
x1= 1.72
x2=( -72 -85.76 ) / 8
x2= -15.5
Ignore negative value
width of sidewalk = 1.72 m