To model the situation of the rectangular zone, we have two pieces of information:

1. The length of the rectangle is 5 cm longer than its width.

   • This means that the length $y$ can be expressed as: $y = x + 5$ where $y$ is the length and $x$ is the width.

2. The total perimeter of the rectangle is 30 cm. The formula for the perimeter $P$ of a rectangle is: $P = 2 \times (\text{Length} + \text{Width})$ Substituting the perimeter and the expressions for length and width: $30 = 2 \times (y + x)$ Now, substitute the expression for $y$ (from the first equation) into the perimeter equation: $30 = 2 \times ((x + 5) + x)$

So, the two equations are:

1. $y = x + 5$
2. $30 = 2 \times (x + 5 + x)$

Let me know if you'd like further details on solving this! Also, here are some related questions for deeper exploration:

1. How can we solve this system of equations to find the values of $x$ and $y$?
2. How would the perimeter change if the length were 10 cm longer than the width?
3. What would happen if the total perimeter were increased to 40 cm?
4. How can we graph these two equations to visually understand the solution?
5. What is the area of the rectangle if the width is found?

Tip: To solve the system, simplify the second equation to find $x$, and then substitute back to find $y$.