SOLUTION: A rectangular plot, bounded on one side by a river, is to be enclosed on the other 3 sides by a fence, and then divided into two equal sized pens by another fence. If you have 900

Question 104187: A rectangular plot, bounded on one side by a river, is to be enclosed on the other 3 sides by a fence, and then divided into two equal sized pens by another fence. If you have 900 feet of fence available, what is the largest are that can be enclosed?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A rectangular plot, bounded on one side by a river, is to be enclosed on the other 3 sides by a fence, and then divided into two equal sized pens by another fence. If you have 900 feet of fence available, what is the largest are that can be enclosed?
:
Perimeter would be:
L + 3W = 900
or
L = (900-3W)
:
Area would be:
A = W * L
Substitute for L
A = W(900-3W)
A = -3W^2 + 900W
:
A quadratic, find the axis of symmetry using: x = -b/(2a); a = -3; b= 900
W = -900/(2*-3)
W = -900/-6
W = 150 ft is the width for max area
:
Find Max area, substitute 150 for W
A = -3(150^2) + 900(150)
A = -3(22500) + 135000
A = -67500 + 135000
A = +67500 sq ft is max area
:
If you graph it: x = width, y = area

:
:
Check it:
L = 900 - 3(150)
L = 900 - 450
L = 450 ft
So it would be 450 by 150: 450*150 = 67500 sq ft
:
Did this help you?
RELATED QUESTIONS
My question is, Math grade 4-8 A rectangular plot is bounded on one side by a straight (answered by Earlsdon)

A rectangular piece of land, bounded on one side by a river, is to be fenced on the other (answered by rfer)

A rectangular plot of farmland is bounded on one side by a river and the other three... (answered by checkley77)

A rectangular plot of farmland is bounded on one side by a river and the other three... (answered by Fombitz)

A field is bounded on one side by a river. A farmer wants to enclose the other three... (answered by nerdybill)

A rectangular field is to be bounded by a fence on three sides and by a straight stream... (answered by ikleyn)

A rectangular plot of the ground is to be enclosed by a fence and then divided down the... (answered by ankor@dixie-net.com)

A rectangular piece of land, bounded on one side by a river, is to be fenced on the other (answered by josgarithmetic)

A rectangular garden bounded on one side by a river is to be fenced on the other three... (answered by ankor@dixie-net.com)