Math CentralQuandaries & Queries


Question from mary, a student:

steven has 100 feet of fencing and wants to build a fence in a shape of a rectangle to enclose the largest possible area what should be the dimensions of the rectangle

Hi Mary,

The area of a rectangle is the length times the width. Suppose the length of the rectangle is $x$ feet then the rectangle has two sides of length $x$ feet so the remaining fencing is $100 - 2x$ feet. This is used for the remaining two sides of the rectangle so these sides are of length $\large \frac{100 - 2x}{2} = 50 - x$ feet each.

Use these dimensions, $x$ feet by $50 - x$ feet to write an expression for the area of the rectangle. What value of $x$ makes this a maximum?


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