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

Algebra.Com
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(52908)   (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 . . .



RELATED QUESTIONS

The width of a rectangle is ¾ its length. The perimeter of the rectangle becomes 50 cm... (answered by mananth,josgarithmetic)
The width of a rectangle is 4 cm less than half its length. If the perimeter of the... (answered by josgarithmetic)
A rectangle has a perimeter of 80 cm. If its width is x, express its length and its area... (answered by stanbon)
the length of a rectangle is 8 cm more than its width if its perimeter is 88 cm what are... (answered by MathLover1)
The area of a rectangle is 28 square inches. If the length and width are both whole... (answered by Fombitz)
The area of a rectangle is 84 square inches. Its length and width are both whole numbers. (answered by scott8148)
if the width of the rectangle is 2 cm more than half of its length and its perimeter is... (answered by rfer)
a rectangle has an area of 480 square feet and its length and width are both whole... (answered by Alan3354)
a rectangle has a length of 6 cm. what is its width if its perimeter and area are the... (answered by checkley71)