Question 411542

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