Question

A rancher wants to construct two identical rectangular corrals using 300 ft of fencing. The rancher decides to build them adjacent to each other, so they share fencing on one side. What dimensions should the rancher use to construct each corral so that together, they will enclose the largest possible area?
easy way. Let the length be 2x and the width be y.
Then 2x=3y=150 maximizes the area
The corral will be 150 by 50 (two 75x50 corrals)

Or, do the math
2x+3y = 300
y = 100 - 2x/3
area a = 2xy = 2x(100 - 2x/3) = 200x - 4/3 x^2
Max area at the vertex of that parabola. Use algebra or calculus.

Related Questions

a rancher has 310 feet of fencing with which to enclose two rectangular corrals, both of the same si... A rancher has 100 meters of fencing to enclose two adjacent rectangular corrals (see figure). The ra... A rancher has 360 feet of fencing to enclose two adjacent rectangular corrals. The wall separating... A rancher wants to construct two identical rectangular corrals using 300 feet of fencing. The Ranger...