First, solve for the total area of the backyard.
Hence, the total area of the backyard is `6000ft^2` .
Then, take half of it to get the area of the pool.
Hence, the area of the pool is `3000 ft^2` .
Also, if x is the width of the walkway, then the dimension of the pool are:
(See image for your reference.)
So, the area of the pool can be express as:
To solve for the value of x, plug-in value of area of pool.
Then expand right side.
Set left side equal to zero.
To simplify the equation further, divide both sides by 4.
Then, apply quadratic formula.
Consider only the value x=10.85, since the other value of x would result to a negative length and width of the swimming pool.
Therefore, the width of the walkway is 10.85 ft.