Maximum-minimum area from a fixed length rope

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Homework Help Overview

The discussion revolves around maximizing and minimizing the area formed by a fixed length rope, specifically focusing on the areas of geometric shapes such as triangles and squares. Participants explore how to allocate the rope length between these shapes to achieve maximum or minimum area configurations.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss different configurations for forming areas, such as starting with a triangle versus a square. They raise questions about the implications of these choices on the resulting areas and whether maximum or minimum areas can be achieved.

Discussion Status

The discussion is ongoing, with various approaches being explored. Some participants have provided insights into the conditions for maximum and minimum areas, while others are questioning the correctness of their calculations and the assumptions made regarding the shapes and their dimensions.

Contextual Notes

There are indications of confusion regarding the definitions of variables and the relationships between the sides of the shapes. Participants are also grappling with the constraints imposed by the total length of the rope and how it is divided among the shapes.

  • #31
And from my answer to the book's, without the L:
$$a=\frac{9}{4\sqrt{3}+9}=\frac{9}{\sqrt{3}(4+3\sqrt{3})}=\frac{3\sqrt{3}\sqrt{3}}{\sqrt{3}(4+3\sqrt{3})}=\frac{9}{4+3\sqrt{3}}$$
Thank you kuruman, Mark, Ray and LCKurtz
 

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