A rancher has 232 feet of fencing to enclose two adjacent rectangular corrals?

A rancher has 232 feet of fencing to enclose two adjacent rectangular corrals. What dimensions will produce the largest total area?


(Enter length and width separated by commas.)


What is the maximum total area?|||I'm assuming that the corrals are about the same size or that they have 1 side in common (say one of the widths).





Let the width = w


Let the lengths = L





Perimeter = 232 = 3w + 4L





Area = 2L*w


2[(232 -- 3w)/4] * w = Area


[116 - 3/2w]*w = Area


116w - 3/2 w^2 = Area





This can be done by completing the square or differentiating. I'm going to differentiate.





3w - 116 = 0


3w = 116


w = 116/3 = 38.666





You can find L from the perimeter formula. Note w might be bigger than L, but it should be less than 2L