SOLUTION: 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 she has 240 meters of fencing and does not fence the side
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Question 167385: 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 she 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? What is the largest area? Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website! 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 =
W =
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
