The floor of a shed given on the right has an area of 105 square feet. The floor is in the shape of a rectangle whose length is 1 foot less than twice the width. Find the length and the width of the foor of the shed.
The length of the floor of the shed is and the width is

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.