Jun has 240 meters of fencing to make a rectangular enclosure. she also wants to use some fencing to split the enclosure into two parts with a fence parallel to two of the sides. what dimensions should the enclosure have to have the maximum possible area? (enter your answers as a comma-separated list.)

Question

Elliana Reilly

Mathematics

14 August, 22:11

Jun has 240 meters of fencing to make a rectangular enclosure. she also wants to use some fencing to split the enclosure into two parts with a fence parallel to two of the sides. what dimensions should the enclosure have to have the maximum possible area? (enter your answers as a comma-separated list.)

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Agustin · Answer 1

Let x meter, y meter be the dimension.

3x+2y=240

y=-3x/2 + 120

The area = - 3 (x^2) / 2 + 120x

=-3/2 (x^2-80x)

=-3/2 (x-40) ^2 + 2400

The area is maximized when x=40

Then y=-3 (40) / 2 + 120 = 60

Hence the required dimension is 40meters, 60meters