Francisco E. answered • 06/21/14

Francisco; Civil Engineering, Math., Science, Spanish, Computers.

The parabola opens down ward and the vertex is located at (0,12), The focal distance is p which can be calculated as y = 11.75 Then the largest distance of the cord will be the two x intersects and this length is given by the equation x=(12-Y)

^{0.5}which has two points one negative and other positive, the length of the base will be (x-(-x)) =2x = 2*(12-Y)^{0.5}The rectangle area will be= Y*(2*(12-Y)

^{0.5}) = 2Y*(12-Y)^{0.5}to maximize I can take the first derivative and equal it to zero or use Solver to obtain the numbers, I picked the second.

I obtained Y =8 and area equals 32; the dimensions are:

height = 8

width = 2*2=4

Check!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!