Question 1158288
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<pre>

The closest analogue is this statement


    Among rectangles with the given perimeter, the largest area has a square with the side length equal one fourth of the perimeter.


From this analogy, 22 = 11 + 11 will provide the greatest possible product 

    11*11 = 121.    


Since they want even numbers, take 22 = 10 + 12, as the closest pair of even numbers to (11,11),

so your answer under given condition will be  (10,12).
</pre>

Solved.


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See the lessons

It is a classic problem on finding maximum value of a quadratic form.


This problem was solved &nbsp;MANY &nbsp;TIMES &nbsp;in this forum.


Therefore, &nbsp;I created lessons at this site, &nbsp;explaining the solution in all details.


The lessons are under these links

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/HOW-TO-complete-the-square-of-a-quadratic-function-to-find-its-minimum-maximum.lesson>HOW TO complete the square to find the minimum/maximum of a quadratic function</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Briefly-on-How-to-complete-the-square-of-a-quadratic-function-to-find-its-minimum-maximum.lesson>Briefly on finding the minimum/maximum of a quadratic function</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/HOW-TO-complete-the-square-to-find-the-vertex-of-a-quadratic-function.lesson>HOW TO complete the square to find the vertex of a parabola</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/Briefly-on-finding-the-vertex-of-a-parabola.lesson>Briefly on finding the vertex of a parabola</A>


&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/A-rectangle-with-the-given-perimeter-which-has-the-maximal-area-is-a-square.lesson>A rectangle with a given perimeter which has the maximal area is a square</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=https://www.algebra.com/algebra/homework/quadratic/lessons/A-farmer-planning-to-fence-a-rectangular-garden-to-enclose-the-maximal-area.lesson>A farmer planning to fence a rectangular garden to enclose the maximal area</A>


Read these lessons attentively.

Consider them as your &nbsp;TEMPLATE.

Having these templates in front of you, &nbsp;solve the &nbsp;GIVEN &nbsp;problem by the same way.


Having it written one time, &nbsp;I do not see any reasons to re-write it again and again with each new given data set or formulation.


By the way, &nbsp;in these lessons, &nbsp;you will find many useful links to accompanied lessons.

Do not miss them.


Consider my lessons as your textbook, handbook, tutorial and (free of charge) home teacher.