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 square meters. What will be the width of the pat

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> 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 square meters. What will be the width of the pat      Log On


   

Question 549292: A garden measuring 12 meters by 16 meters is to have a pedestrain 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) About Me  (Show Source):
You can put this solution on YOUR website!
Let the width of sidewalk be x
..
Length of garden = 16 m
Width =12m
285-96=189 m^2
Area =96m^2
Area of sidewalk =189 m^2
Length of ground + sidewalk =16
width of ground + sidewalk = 12+2x

( 16+2x )(12+2x )-189=96

192+32x +24x+4X^2-189 = 96
4X^2+56 x-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
sqrt%28%094624%09%29= 68
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=( -56 + 68 )/ 8
x1= 1.5
x2=(-56 -68) / 8
x2= -15.5
Ignore negative value
width of sidewalk = 1.5 m