Question 411542: A rectangular grass lawn, 45 m long and 38 m wide, has a uniform concrete path around it. If the area of the concrete path is 440 m^2, find the width of the concrete path.
PLEASE HELP!!! i need your solutions :(
Answer by sudhanshu_kmr(1152)   (Show Source):
You can put this solution on YOUR website!
Let the width of the concrete path is x meter.
now, for whole area including path and lawn :
length = 45 + 2x
width = 38 + 2x
area of concrete path = whole area - lawn area
= (45+2x)*(38+2x) - 45*38
= 90x + 76x + 4x^2
according to question ,
90x + 76x + 4x^2 = 440
=> 4x^2 + 166x - 440 = 0
=> 2x^2 + 83x - 220 = 0
=> 2x^2 + 88x - 5x - 220 = 0
=> 2x(x+44) - 5(x+44) = 0
=> (2x-5)(x+44)=0
so, x = 5/2 , -44
second value is not possible,
width of path = 5/2 m = 2.5 m
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