SOLUTION: A rancher needs to enclose two adjacent rectangular corrals, one for cattle and one for sheep. If the river forms one side of the corrals and 330 yd of fencing is available, what i

Question 232503: A rancher needs to enclose two adjacent rectangular corrals, one for cattle and one for sheep. If the river forms one side of the corrals and 330 yd of fencing is available, what is the largest total area that can be enclosed?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
A rancher needs to enclose two adjacent rectangular corrals, one for cattle and one for sheep. If the river forms one side of the corrals and 330 yd of fencing is available, what is the largest total area that can be enclosed?
:
Let W = the three sides to make the width of the two corrals
Let L = the one side parallel to the river
:
L + 3W = 330 yds (of fence available)
L = (330-3W); this form for substitution
;
Area
A = L * W
Replace L with (330-3W)
A = (330-3W) * W
A = -3W^2 + 330W
A quadratic equation, the axis of symmetry will be the value for max area
Find that using x = -b/(2a)
In this equations: x = W; a = -3; b = 330
W =
:
W =
W = +55 yd is the width for max area
:
Find the max area, substitute 55 for W in the area equation:
A = -3(55^2) + 330(55)
A = -3(3025) + 18150
A = -9075 + 18150
A = +9075 sq/yds is max area
;
:
Check this; Find the length
L = 330 - 3(55)
L = 330 - 165
L = 165 yds
;
Find the area: 165 * 55 = 9075 sq/yds
RELATED QUESTIONS
A rancher needs to enclose two adjacent rectangular corrals, one for cattle and one... (answered by ikleyn)

a rancher has 360 yds of fencing with which to enclose two adjacent rectangular corrals-... (answered by ankor@dixie-net.com)

A rancher needs two adjacent corrals, one for cattle and one for sheep. If a river forms... (answered by Alan3354)

a rancher has 180 ft of fencing to enclose two adjacent rectangular corrals. A river... (answered by ankor@dixie-net.com)

A farmer wants to enclose two adjacent rectangular regions next to a river, one sheep and (answered by ankor@dixie-net.com)

I have tried and tried to solve this and another problem. I am in college and on the... (answered by josmiceli)

I have a problem on a study guide that I need help with. A rancher wants to enclose... (answered by ewatrrr)

A rancher has 100 meters of fencing to enclose two adjacent rectangular corrals. The... (answered by scott8148)

A rancher has 1200 feet of fencing to enclose two adjacent rectangular corrals of equal... (answered by ikleyn,advanced_Learner)