SOLUTION: A rectangular lot is to be bounded by a fence on three sides and by a wall on the fourth side. Two kinds of fencing will be used with heavy duty fencing selling for $4 a foot on th
Algebra.Com
Question 551630: A rectangular lot is to be bounded by a fence on three sides and by a wall on the fourth side. Two kinds of fencing will be used with heavy duty fencing selling for $4 a foot on the side opposite the wall. The two remaining sides will use standard fencing selling for $3 a foot. What are the dimensions of the rectangular plot of greatest area that can be fenced in at a cost of $6600?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A rectangular lot is to be bounded by a fence on three sides and by a wall on the fourth side.
Two kinds of fencing will be used with heavy duty fencing selling for $4 a foot on the side opposite the wall.
The two remaining sides will use standard fencing selling for $3 a foot.
What are the dimensions of the rectangular plot of greatest area that can be fenced in at a cost of $6600?
:
The perimeter
P = L + 2W
The cost
4L + 3(2W) = $6600
4L + 6W = $6600
4L = (6600-6W)
divide both sides by 4
L = 1650 - 1.5W
:
The area:
A = L * W
Replace L with (1650-1.5w)
A = W(1650-1.5W)
A quadratic equation
A = -1.5w^2 + 1650w
Find the axis of symmetry: x = -b/(2a); In this equation: a=-1.5; b=1650
w =
w = +550 ft is the width
find the length
L = 1650 - 1.5(550)
L = 825 ft is the length
:
An area 825 by 550 ft gives max area for $6600
:
:
:
See if this checks out
4(825) + 3(2(550)) =
3300 + 3300 = $6600
RELATED QUESTIONS
A rectangular field is to be bounded by a fence on three sides and by a straight stream... (answered by ikleyn)
A rectangular garden bounded on one side by a river is to be fenced on the other three... (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 rfer)
A rectangular plot, bounded on one side by a river, is to be enclosed on the other 3... (answered by ankor@dixie-net.com)
A college is planning to construct a rectangular parking lot on land bordered on one... (answered by josgarithmetic)
A farmer has 336 running feet of fence and wishes to form a rectangular pasture. one side (answered by Fombitz)
A store wants to construct rectangular parking lot on land bordered on one side by a... (answered by checkley77)
A college is planning to construct a rectangular parking lot on land bordered on one side (answered by josmiceli)
A college is planning to construct a rectangular parking lot on land bordered on one... (answered by josgarithmetic)