Question

Find the dimensions of the rectangle of maximum area that can be formed from a 210-in. piece of wire. (Use decimal notation. Give your answer to three decimal places.)
Does this problem require optimization over a closed interval or an open interval?


A. open


B. closed

Answer 1

Answer:

  52.500 by 52.500 inches

Step-by-step explanation:

The rectangle with maximum area will be a square. Its side length will be 1/4 the perimeter, so is 210/4 = 52.5 inches.

The figure is a 52.500 inch square. The interval of optimization is closed.

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Side lengths are restricted to the interval 0 to 105 inches.

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Any n-sided polygon with a given perimeter will have its maximum area when the polygon is regular. A regular 4-gon is a square.