Find the dimensions of the rectangle of maximum area that can be formed from a 210-in. piece of wire. (Use decimal notation. Giv
e your answer to three decimal places.)
Does this problem require optimization over a closed interval or an open interval?
A. open
B. closed
1 answer:
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 <em>closed</em>.
_____
Side lengths are restricted to the interval 0 to 105 inches.
__
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.
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a) 2/6 * 1/5 = 2/30 = 1/15
b) 1/15 + 2/6 * 1/5 = 2/15
