Step 1 :We are given that the area of the floor of the shed is 105 square feet and the length is 1 foot less than twice the width. We can denote the width as \(w\) and the length as \(l\).
Step 2 :We can set up a system of equations to solve for the length and width. The first equation is \(l * w = 105\) and the second equation is \(l = 2w - 1\).
Step 3 :We substitute the second equation into the first one to solve for \(w\), and then use the value of \(w\) to find \(l\).
Step 4 :Solving the equations, we get two possible values for \(w\), -7 and \(\frac{15}{2}\), and one possible value for \(l\), -15.
Step 5 :However, the negative value for width and length doesn't make sense in this context as dimensions cannot be negative. We should only consider the positive solution.
Step 6 :So, the width of the floor of the shed is \(\frac{15}{2}\) feet and the length is \(2*(\frac{15}{2}) - 1 = 14\) feet.
Step 7 :Final Answer: The width of the floor of the shed is \(\boxed{\frac{15}{2}}\) feet and the length is \(\boxed{14}\) feet.