posted by amber .
a rancher has 310 feet of fencing with which to enclose two rectangular corrals, both of the same size. the two corrals will share one side, and a barn forms one side of both corrals. suppose the width of each corral is X feet. express the total area of the two corrals as a function of X.
assuming the barn forms the "length" of each corral, then the total fencing used comprises three widths and two lengths.
Letting x be the width and y the length,
3x + 2y = 310
y = (310-3x)/2
the area of each corral is width * length, so the total area is 2xy
area = 2xy = 2x * (310-3x)/2 = x(310-3x)