SOLUTION: a factor is to built on a lot measuring 180 ft by 240 ft. Building code specifies that a lawn of uniform width and equal in area to the factory must surround the factory. What must

Algebra ->  Vectors -> SOLUTION: a factor is to built on a lot measuring 180 ft by 240 ft. Building code specifies that a lawn of uniform width and equal in area to the factory must surround the factory. What must      Log On


   

Question 49846: a factor is to built on a lot measuring 180 ft by 240 ft. Building code specifies that a lawn of uniform width and equal in area to the factory must surround the factory. What must the width of this lawn be and what are the dimensions of the factory?
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
a factor is to built on a lot measuring 180 ft by 240 ft. Building code specifies that a lawn of uniform width and equal in area to the factory must surround the factory. What must the width of this lawn be and what are the dimensions of the factory?
LET WIDTH OF LAWN =X
HENCE LENGTH OF FACTORY AREA=240-X-X=240-2X
WIDTH OF FACTORY AREA =180-X-X=180-2X
AREA OF FACTORY =(240-2X)(180-2X)=4(X-120)(X-90)
TOTAL AREA OF LOT =180*240
HENCE AREA OF LAWN =180*240-4(X-120)(X-90)=AREA OF FACTORY=4(X-120)(X-90)
HENCE
8(X-120)(X-90)=180*240
X^2-210X+90*120-30*180=0
X^2-210X+5400=0
(X-30)(X-180)=0
X=30...OR...180...SINCE X=180 GIVES ABSURD RESULT,
X=30 IS THE ANSWER