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You are to fence off two rectangular garden beds of the same size in such a way that they share one side. Given that you have 120m of fence, what is the maximum total area (in m2) that vou can fence off in this way?

You are to fence off two rectangular garden beds of the same size in such a way that they share one side. Given that you have 120m of fence, what is the maximum total area (in m2) that vou can fence off in this way?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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**Problem Statement:** You are to fence off two rectangular garden beds of the same size in such a way that they share one side. Given that you have 120 meters of fence, what is the maximum total area (in m²) that you can fence off in this way? **Diagram Explanation:** The diagram depicts two adjacent rectangular areas that share one side. The shared side is vertical, and both rectangles have the same dimensions. The width of the rectangles is denoted as \( x \), and the height is \( y \). - There are two vertical sections (each \( y \)) and three horizontal sections (each \( x \)) to be fenced, as both rectangles share one vertical side. **Mathematical Constraints:** 1. Total fencing used: \( 3x + 2y = 120 \). 2. Area to be maximized: \( 2xy \). This involves optimizing the values of \( x \) and \( y \) to maximize the fenced area while adhering to the fencing constraint.
Transcribed Image Text:**Problem Statement:** You are to fence off two rectangular garden beds of the same size in such a way that they share one side. Given that you have 120 meters of fence, what is the maximum total area (in m²) that you can fence off in this way? **Diagram Explanation:** The diagram depicts two adjacent rectangular areas that share one side. The shared side is vertical, and both rectangles have the same dimensions. The width of the rectangles is denoted as \( x \), and the height is \( y \). - There are two vertical sections (each \( y \)) and three horizontal sections (each \( x \)) to be fenced, as both rectangles share one vertical side. **Mathematical Constraints:** 1. Total fencing used: \( 3x + 2y = 120 \). 2. Area to be maximized: \( 2xy \). This involves optimizing the values of \( x \) and \( y \) to maximize the fenced area while adhering to the fencing constraint.
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