Geometric Constraints Math Example 2

Solution

1. 1
   Step 1: Perimeter constraint: $2x + 2y = 36 \Rightarrow y = 18 - x$.
2. 2
   Step 2: For a valid rectangle, both sides must be positive: $x > 0$ and $y = 18 - x > 0 \Rightarrow x < 18$.
3. 3
   Step 3: Therefore $x \in (0, 18)$. The constraint also implies $y = 18 - x \in (0, 18)$.
4. 4
   Step 4: Note: if $x = 9$ then $y = 9$ (a square), the special symmetric case.