SOLUTION: Rock had 800 foot fence material. He wants to form a rectangular closure or casing and then divides it into 3 section by running 2 lengths of fence parallelized to one side. What m
Algebra.Com
Question 1082918: Rock had 800 foot fence material. He wants to form a rectangular closure or casing and then divides it into 3 section by running 2 lengths of fence parallelized to one side. What must be the dimension of the enclosure be in order to maximize the enclosed area?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Rock had 800 foot fence material.
He wants to form a rectangular closure or casing and then divides it into 3 section by running 2 lengths of fence parallelized to one side.
What must be the dimension of the enclosure be in order to maximize the enclosed area?
:
let L = the length of the enclosure
let w = the width and the 2 dividing fences
;
2L + 4w = 800
simplify, divide by 2
L + 2w = 400
L = 400-2w, use this form for substitution
:
Area = L * w
replace L with (400-2w)
A = (400-x)*2w
A quadratic equation
A = -2w^2 + 400w
Max area occurs on the axis of symmetry, find that using x =-b/(2a)
w =
w = +100 ft is the width for max area
and
L = 400-2(100)
L = 200 ft is the length
RELATED QUESTIONS
a farmer needs to enclose a rectangular field with a fence down the middle to divide it... (answered by ikleyn,Edwin McCravy)
a rectangular plot ground is to be enclosed by a fence and then divided down the middle... (answered by ikleyn)
A homeowner wants to enclose a 5,300 square foot rectangular garden by a fence in his... (answered by ankor@dixie-net.com)
Tex wants to make a lawn in . He buys enough sod to make a 10 foot by 30 foot rectangular (answered by stanbon)
This problem is in the review section about the farmer and fencing.
A farmer with... (answered by Alan3354,stanbon)
James has 66 yards of fencing. Each fence panel is 3/4 yard long. James wants to fence a... (answered by josmiceli)
Joe wants to put a fence around his rectangular garden. His garden measures 33 ft by 39... (answered by malglu)
Jose wants to put a fence around his rectangular garden. His garden measures 33 feet by... (answered by josmiceli)
A fence is to be built to enclose a rectangular area of 290 square feet. The fence along (answered by ankor@dixie-net.com)