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what is the colour amber - Network4

📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 After reducing each side by 4 cm, the new side is $s - 4$, and the new area is:

📌 This is complex, so instead, express the final answer directly in terms of $A$ and $s$, noting that:

📌 This is the decrease in area, but for olympiad style, the cleanest boxed final answer in terms of $A$ is:

📌 ---Question: A cartographer is creating a rectangular map with a fixed perimeter of 100 km. What is the largest possible area (in square kilometers) of the map that can be represented under this constraint?

📌 Solution: Let the length and width of the rectangle be $ x $ and $ y $, respectively. The perimeter is given by:

📌 Substitute $ y = 50 - x $ into the area formula:

📌 This is a quadratic function opening downward, so the maximum occurs at the vertex:

📌 Then $ y = 50 - x = 25 $, so the rectangle is a square. The maximum area is:

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