SOLUTION: A rancher has 840 feet of fencing to construct 6 corrals. FInd the dimensions that maximize the enclosed area. What are the dimensions? What are the larger dimensions, smaller dime
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Question 914250: A rancher has 840 feet of fencing to construct 6 corrals. FInd the dimensions that maximize the enclosed area. What are the dimensions? What are the larger dimensions, smaller dimensions and area?
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
Does more information come with this question? Six separate corrals, not connected to each other?
Maybe x and y, dimensions of each corral, all corrals congruent. ASSUMING rectangle shape.
The fencing is the sum of the perimeters.
Total area,
Substitute for either variable, choosing y, in the area equation:
Do some steps,
, but maybe not necessary in that form.
A is a parabola opening downward having a vertex as a maximum point, which is what you want to solve for. Find the roots!
Roots are 0 and 70.
The vertex will be for the exact middle of these roots, which will be .
Notice that according to the earlier found equation from perimeter, x+y=70, which means that also .
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Each corral will be a square with side 35 feet.
Based on the questions part of what you posted, some of the description is missing and so maybe the answer I found does not fit what you really were given. I could only assume that your six corrals would be rectangles and not connected to each other. Otherwise, give the complete problem description.
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