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

##### 1 Answer

Feb 7, 2017

#### Explanation:

Let the length of one side of the rectangle be

Then the opposite side is also 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,

Hence the rectangle of maximum area is a