How do you find the dimensions of the rectangle of greatest area whose perimeter is 20 cm?

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Answer 1 · 2017-02-07T20:35:32

#5 "cm" xx 5 "cm"#

Let the length of one side of the rectangle be #x# #"cm"#.

Then the opposite side is also of length #x# #"cm"#, while the two other sides are of length:

#(20-2x)/2 = 10-x# #"cm"#

The area of the rectangle is:

#x(10-x) = 10x-x^2 = 25-25+10x-x^2 = 25-(x-5)^2# #"cm"^2#

This attains its maximum, #25#, when #x=5#

Hence the rectangle of maximum area is a #5 "cm" xx 5 "cm"# square.