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

Question

7472 views around the world

You can reuse this answer
Creative Commons License

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.