Step 1 :Given that the total length of the fencing is 100 ft and the length of the dog run is 5 times its width, we can set up a system of equations to find the dimensions of the dog run.
Step 2 :Let's denote the width as \(w\) and the length as \(l\). We have two equations:
Step 3 :1. \(l = 5w\) (from the condition that the length is 5 times the width)
Step 4 :2. \(2*(l + w) = 100\) (from the condition that the total length of the fencing is 100 ft)
Step 5 :We can substitute the first equation into the second to solve for \(w\), and then use the value of \(w\) to find \(l\).
Step 6 :Substituting \(l = 5w\) into the second equation, we get \(2*(5w + w) = 100\), which simplifies to \(12w = 100\).
Step 7 :Solving for \(w\), we get \(w = \frac{25}{3}\).
Step 8 :Substituting \(w = \frac{25}{3}\) into the first equation, we get \(l = 5 * \frac{25}{3} = \frac{125}{3}\).
Step 9 :Final Answer: The dimensions of the dog run are \(\boxed{\frac{25}{3} \text{ ft}}\) wide and \(\boxed{\frac{125}{3} \text{ ft}}\) long.