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

Algebra ->  Quadratic Equations and Parabolas -> 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      Log On


   

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) About Me  (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 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 pathway = 1.5 m
m.ananth@hotmail.ca