SOLUTION: a rancher removed 200 ft of fence from a field on his ranch. he wishes to reuse teh fencing to create a rectangular corral into which he will build a 6 ft wide wooden gate. what di
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Question 204730: a rancher removed 200 ft of fence from a field on his ranch. he wishes to reuse teh fencing to create a rectangular corral into which he will build a 6 ft wide wooden gate. what dimensions will result in the greatest possible area?
You can put this solution on YOUR website! rancher removed 200 ft of fence from a field on his ranch.
he wishes to reuse the fencing to create a rectangular corral into which he
will build a 6 ft wide wooden gate.
what dimensions will result in the greatest possible area?
:
Let the side with the gate = (L-6)
then:
L + (L-6) + 2W = 200
:
2L + 2W = 200 + 6
:
2L + 2W = 206
Simplify, divide by 2
L + W = 103
W = (103-L)
:
The Area equation: A = L * W
Replace W with (103-L)
A = L(103-L)
A = -L^2 + 103L
Find the max area by finding the axis of symmetry
L =
L = +51.5, length for max area
Find W:
W = 103 - 51.5
W = 51.5
:
Dimensions for max area: 51.5 by 51.5
:
Check: 51.5 + (51.5-6) + 2(51.5) = 200
