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

Question 549521: A garden measuring 12 meters by 16 meters is to have a pedestrian pathway installed all around it, increasing the total area to 285 square meters. What will be the width of the pathway?
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!
Area of garden = 12*16= 192 sq.m
lenngth including pathway = 16+2x
width including pathway = 12+2x
Total area = (16+2x)(12+2x)
Total area =285
(16+2x)(12+2x)=285
192+32x+24x+4x^2=285
4x^2+56x+192=285
4x^2+56x-93=0
Find the roots of the equation by quadratic formula
a= 4 b= 56 c= -93
b^2-4ac= 3136 + 1488
b^2-4ac= 4624 = 68

x1=( -56 + 68 )/ 8
x1= 1.5
x2=( -56 -68 ) / 8
x2= -15.5
Ignore negative value
width of pathway = 1.5 m
m.ananth@hotmail.ca

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