Math CentralQuandaries & Queries


Subject: area
Name: kyle
Who are you: Student

paul has enough material to make a fence 22 feet long. he will use this material to
fence of a rectangular section of his yard. the rectangles sides must all be whole numbers.
i am having a hard time finding the greatest and the least area that he can enclose his fence

Hi Kyle,

If you have 22 ft of material to fence a rectangular section, then the width of the rectangle plus the height must be half of that [WHY?] - so, 11 ft. Since you are told the sides must have whole number lengths, you have just a few possibilities to check:

width height
1 10
2 9
3 8
4 7
5 6

You can test each pair to see which gives you the largest and smallest areas.

This method would probably not be a good approach if you didn't know that the sides must be whole numbers.


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