SOLUTION: The width and the length of a rectangle are both prime numbers. What is its maximum area when its perimeter is 40 cm?

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Question 1173769: The width and the length of a rectangle are both prime numbers. What is its maximum area when its perimeter is 40 cm?
Answer by ikleyn(52898) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let p and q be that prime integer numbers that are the length and the width, respectively.


Then you have 

    p + q = 40/2 = 20,


and (OBVIOUSLY) you should select these prime numbers p and q as close to their mean value of 10 as possible.



Just the first trial  13 and 7  leads you to the success and to the dimensions  p= 13,  q=  7  centimeters.



ANSWER.  The area of the rectangle is  13*7 = 91 cm^2.

Solved.

I'd say that everything is simple in this problem, and there is nothing extraordinary interesting . . .