Say the area of the lawn is , and the area of the path is . We are given the dimensions of the lawn, so .
Now you know that .
Let us define a function that gives the area of the concrete path with respect to some width, denoted . After investigation, we find that this function is defined by : . You are trying to find such as . Solve for :
Using the quadratic formula :
A width can only be positive, so discard the negative solution. You just found the width of the concrete path
Does that make sense ?