Math CentralQuandaries & Queries


Question from Almarie, a student:

Lauren has 40 feet of metal fencing material to fence three sides of a rectangular garden. A tall wooden fence serves as her fourth side. Write a function for the area of the garden A in terms of x, the width in feet.


I think the first step is to draw a diagram and this soon shows that the problem is not clear. Does the tall wooden fence form a long side of the garden,


or a short side of the garden


It's not clear so I think there are two answers.

In either case the area of a rectangle is the length times the width and the width can't be larger than the length. In my second diagram if the width is x feet and the total amount of metal fencing is 40 feet then how much is left for the other two sides? That's the amount for the two long sides so how much for one long side? Now you know the length of a long side (the length) and the short side (the width) what is the area?

Now look at the situation described by my first diagram. If x feet is the length of a short side can you find an expression for the area?


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