SOLUTION: To make an enclosure for chickens, a rectangular area will be fenced next to a house. Only 3 sides will need to be fenced. There is 160 ft of fencing material. What dimensions will

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Question 882967: To make an enclosure for chickens, a rectangular area will be fenced next to a house. Only 3 sides will need to be fenced. There is 160 ft of fencing material. What dimensions will maximize the area of the enclosure?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = the length of
one of the opposing sides
+160+-+2x+ = the length
of the 3rd side
-------------------------------
+A+=+x%2A%28+160+-+2x+%29+
+A+=+-2x%5E2+%2B+160x+
--------------------------
When the form of the equation is
+f%28x%29+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c+
The max is at +x+=+-b%2F%282a%29+
----------------------------------
+x%5Bmax%5D+=+-160+%2F+%282%2A%28-2%29%29+
+x%5Bmax%5D+=+40+
and
+160+-+2x+=+160+-+80+
+160+-+2x+=+80+
----------------------
The 3 sides are 40, 40, and 80
Here's the plot:
+graph%28+400%2C+400%2C+-10%2C+100%2C+-500%2C+5000%2C+-2x%5E2+%2B+160x+%29+