<PRE><B>Question 167385</B>
A farmer wants to build two rectangular pens of the same size next to a river so
 that they are separated by one fence. If he has 240 meters of fencing and does
 not fence the side next to the river, what are the dimensions of the largest area
 she can enclose?
:
We will have 3 sides = to the width (W), and 1 side equal to the length:
Fencing equation:
3W + L = 240
:
L = 240-3W
:
Area = L*W
Substitute (240-3W) for L
A = (240-3W)* W
A = -3W^2 + 240W
:
Max area occurs at the axis of symmetry of this equation
W = {{{(-240)/(2*-3)}}}
W = {{{(-240)/(-6)}}}
W = 40 ft
:
Find L
L = 240-3(40)
L = 240 - 120
L = 120 ft
:
 What is the largest area?
;
120 * 40 = 4800 sq/ft
:
:
you can also confirm this in the equation, substitute 40 for W</PRE>