Geometry: An Interactive Journey to Mastery

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does not lose energy as it bounces, that there is no drag due to
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Of all rectangles of perimeter 100 centimeters, which has the
largest area?
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We can write the dimensions of the rectangle as
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7KHQWKHDUHDRIWKHUHFWDQJOHLVͼ௘x௘ͽͼ௘íx௘ͽ íx^2 ,
which is clearly as large as it can be when x = 0—in which
case the rectangle is a 25 × 25 square.
Comment: Think about the dual problem: Of all rectangles of
area 100 square centimeters, which has the least perimeter?
The answer turns out to be a square, but proving this is
not straightforward.
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x This lesson is purely optional, and this topic does not appear in typical geometry courses. There are
no recommended study tips for this lesson other than to enjoy the lesson and let the thinking about it
strengthen your understanding of geometry as a whole.
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x Don’t forget to have fun in your thinking of mathematics. This is a fun topic.

A

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Figure 27.3

íx íx

25 + x

25 + x

Figure 27.4