Arancher 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.

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

49.5 and -0.5

Step-by-step explanation:

a  + b =49

a -  b = 0.5

a= 49.5

b= -0.5