A square of lawn is surrounded by a path 0.5m wide,,the area of the lawn is 23m^2 bigger than that of the area of the path ,,find the side of the lawn.
If the lawn has side x meters, then
lawn area: x^2
total area: (x+1)^2
path area: (x+1)^2-x^2 = 2x+1
So, we have
x^2 = 2x+1 + 23
Now just find x.