There is 6yd of fencing to enclose 2 adjacent rectangular corrals of = area. Fencing is used to separate the corrals no fencing is along the river.

Question

what dimensions for one of the individual corrals will produce the largest total area? What is the mac are for the 2 corrals combined? There should by 3 x’s & 1 y in the equation. Please complete fully and explain. Confused!! 

Answer 1

suppose the total length is L yards.

 

sketch the two corrals. there are three widths and one overall length (which I designated as 2w) // to the river.

Each area is xw (two equal rectangular corrals).

 

Perimeter equation (using up all of the available fencing):  3w + 2x = L so x = ½(L - 3w)

 

area xw, to be maximized, is f(w) =   ½w(L - 3w).  Remember, L is a constant (6 yd, according to you)

 

f(x) is a parabola and its vertex is the maximum value.  Now can you complete the work?