Karl benedic, the presidentof mathematics club, proposed a project: to put up a rectangular math garden whose lot perimeter is 36 meters.

Question

He was soliciting suggestions from the members for feasible dimensions of the lot. Suppose you are a member of the club, what will you suggest to Karl Benedic if you want a maximum lot area? You must convince him through a mathematical solution.

Answer 1

Let the length be L and the width W. The area is LW.

When is the area maximum? Now let L be greater than W so that L=W+x where x≥0.

We can write W=L-x and A=L(L-x)=L^2-Lx. The right-hand expression has the greatest value when x=0 and A=L^2, so when the rectangle is a perfect square we have the maximum area.