A rancher is adding a corral to his barn so that the barn opens directly into the corral. He has 195 feet of fencing left over from another project. Find the greatest possible area for his corral using this length of fence. (Hint: The corral with maximum area is not a square) :roll:
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- Thread starter Endria
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Endria said:A rancher is adding a corral to his barn so that the barn opens directly into the corral. He has 195 feet of fencing left over from another project. Find the greatest possible area for his corral using this length of fence. (Hint: The corral with maximum area is not a square) :roll:
Well, with what is given in your problem, Ben Cartwright can use the barn
door as the entrance to the corral, so that the fence forms a circle with
a short chord being the width of the door !
However, the chord must be "wide" enuff to let big Hoss get through.
Seriously, looks like the fence would be connected to 2 corners of the
barn; let b = the length of that barn side.
Then the fence forms an almost circle, b being a chord.
(I'm using circle because a circle has larger area than a square; same perimeter).
Then I see no choice but to calculate the area in terms of b.
"Thanks a lot.
I don't find the way to draw here.
That corral must be ractangular and three sides without side of barn.please reply again. endria"
Please don't PM in that manner; POST instead.
If your corral must be rectangular with the barn being one side,
why didn't you say so right off the bat?
barn side = b (so another side has to equal b);
that leaves (195 - b) / 2 as the other 2 sides.
So area = b * [(195 - b) / 2] = (195b - b^2) / 2
Maximums (or minimums) don't apply here: if they do,
then something wrong with your question.
Like, how do you expect an actual value as answer when
we don't know the length of barn's side?
I don't find the way to draw here.
That corral must be ractangular and three sides without side of barn.please reply again. endria"
Please don't PM in that manner; POST instead.
If your corral must be rectangular with the barn being one side,
why didn't you say so right off the bat?
barn side = b (so another side has to equal b);
that leaves (195 - b) / 2 as the other 2 sides.
So area = b * [(195 - b) / 2] = (195b - b^2) / 2
Maximums (or minimums) don't apply here: if they do,
then something wrong with your question.
Like, how do you expect an actual value as answer when
we don't know the length of barn's side?