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| Math Central | Quandaries & Queries |
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Question from Carisa, a parent: Ms. Zoe has a few dilemmas. She plants a garden each yr. & last yr. the rabbits ate her tomato plants. She has limited space which is 8ft by 4ft. & wishes to maximize the space. Ms. Zoe is considering 3 possible shapes. Those shapes are a rectangle, a triangle, or a polygon. She needs to buy fencing materia to enclose the garden & wants to get the biggest bang for her money. Each tomatoe plant req. 4 sq.ft to so she needs to know the # of plants to purchase & also needs to how much fence to buy. |
Carisa,
This problem does not seem to make sense. Some of the apparent options are not meaningful.
If her available space is "8 feet by 4 feet" it does not seem
as if she has any choice of the shape! She has a rectangular plot of 32 square feet, and this divides evenly into 4 square foot plots (how many?).
It may be shown that she cannot save fence by including extra space inside the fence as well as the 4x8 rectangle.
If she could use an arbitrary 32 square foot plot it would be most efficiently fenced as a circle and this can be approached arbitrarily closely by a polygon with many sides.
-RD
Carisa,
There is an expression for the area of a regular polygon at
http://mathcentral.uregina.ca/QQ/database/QQ.09.06/s/dana1/dana1.html
Harley
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