Question

A rancher has 4 comma 700 feet of fencing available to enclose a rectangular area bordering a river. he wants to separate his cows and horses by dividing the enclosure into two equal areas. if no fencing is required along the​ river, find the length of the center partition that will yield the maximum area.

Answer 1

Area=length*width
let the sides perpendicular to the river be x
then the side parallel to the river is 4,700-2x
A(x)=x(4700-2x)
A(x)=4700x-2x^2

This a quadratic function with a=-2 and b=4700
thus
Maximum area occurs where x=-b/2a=-4700(-2*2)=1,175 ft
length=4700-2(1175)=2,350 ft