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Cyberpunk Math Lab: The Non-Linear World FREE
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Area & Perimeter with Algebra
Learning Objectives
- Write expressions for area and perimeter
- Optimize dimensions
- Solve geometric equations
Key Concepts
Perimeter
P = 2l + 2w for rectangles
Area
A = l × w for rectangles
Theory
**Using algebra with geometry:**
Given constraints, write equations:
- If P = 40: 2l + 2w = 40 → l + w = 20 → w = 20 - l
- Then A = l(20 - l) = 20l - l²
**Maximum area** of a rectangle with fixed perimeter is always a **square**.
- P = 40 → max area when l = w = 10, A = 100
Examples
Rectangle: perimeter 24, find max area
Solution: l = w = 6, A = 36 (square)