A square lawn surrounded by a walkway of uniform width of 2 meters

Question

A square lawn has side length of x meters, it is surrounded by a walkway of uniform width on all sides, the width of the walk way is 2 meters, if the area of the lawn is the same as the area of the walk way, what is the side length of the walkway

Answer 1

let x = side of lawn area

 

Since the lawn area is a square, then the area of the lawn is = x.x = x²

 

The side of the lawn and walkway = x + 2m+2m = x+4

 

The area of the lawn and walkway = (x+4).(x+4) = ( x+4)²

 

The area of the walkway is then = Area of lawn and walkway - Area of the lawn

 

That is Area of walkway = (x+4)² - x²

 

since the area of the lawn is = to the area of the walkway

 

x²=(x +4)²-x² , Rearranging x²+x²=(x+4)²

 

2x²=x²+8x+16, Rearranging, x²-8x-16=0

 

solving quadratic equation , a=1, b=-8, c=-16

 

find Δ = b² - 4ac = (-8)² -4(1)(-16) = 64 + 64 = 128

 

x=-b±√Δ/2a = (8 ± √128)/2  = (8 ± 11.3) /2 = 9.65 m

 

where x is the length of the side of the lawn 

 

The length of the sidewalk is thus x+2m+2m = 

                                                 

9.65m+2m+2m= 13.65m