Hello,

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 ?