Step 1 :The problem is asking for the length of the garden, which is represented by x. The equation given is a quadratic equation, which can be solved by factoring, completing the square, or using the quadratic formula. In this case, the equation is already in the form of a product equal to a constant, so it can be solved by factoring.
Step 2 :Set up the equation: \(x(x - 4) = 140\)
Step 3 :Solve the equation to find the possible values of x. The solutions to the equation are -10 and 14.
Step 4 :However, since the length of a garden cannot be negative, discard the negative solution.
Step 5 :Final Answer: The length of the garden is \(\boxed{14}\) feet.