posted by Khelany on .
A rectangular rice land is to be fenced along 4 sides and in the middle to divide it into to 2 equal areas. If 200m of fencing is available, what is the maximum area to be fenced?
Assume that length l is greater than or equal to width w. Assert that the dividing fencing must be equal to the width (ie it must be perpendicular) by reasoning that if it were at any other angle, it would be longer, and the length would be reduced.
A = w * l
200 = 3w + 2l
.: A = w*(200-3w)/2
or A = 100 w - (3/2) w^2
Take the derivative and find when this is 0.
0 = (d/dw) (100 w-(3/2)w^2)
Solve for w, use to determine A
where did you get the 3w
The 200m fencing is used for two length-sides (l), two width-sides (w) and the middle divider (w).
This: 200 = 2l + 3w