Bulletin Board's Maximum Area

Question

An elementary school teacher wishes to use 13 feet of scalloped border to enclose a rectangular region on her bulletin board. What is the maximum area that she can enclose with the border.

Answer 1

P = 13 = 2L + 2w

(13/2) = L + w

13/2 - L = w

Area = length x width

= (13/2 - w)*w

= (13/2)w - w^2

Max occurs at the AVERAGE of the zeros, which are w=0 and w=13/2.

So the max occurs at w=(13/2+0)/2 = 13/4

Max area is (13/2 - 13/4)*13/4 = (26/4 - 13/4)*(13/4) = 13/4 * 13/4 = 169/16