Measurement:
A dog kennel owner has $100 \mathrm{ft}$. of fencing to enclose a rectangular dog run. She wants it to be 5 times as long as it is wide. Find the dimensions of the dog run. What is the perimeter of the dog run?

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.