SOLUTION: roger has 144 feet of fencing material to enclose a rectangular exercise yard for his dog. one side of the yard will border his house, so he will only need to fence three sides. fi

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Question 690215: roger has 144 feet of fencing material to enclose a rectangular exercise yard for his dog. one side of the yard will border his house, so he will only need to fence three sides. find the maximum area of the yard?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
There is a side parallel to the house and there
are 2 equal sides perpendicular to the house
Call each of the sides perpendicular
to the house +s+
The side parallel to the house is
+144+-+2s+ ft long
The area, +A+ is
(1) +A+=+s%2A%28+144+-+2s+%29+
(2) +A+=+-2s%5E2+%2B+144s+
This is a parabola with a maximum, because of
the minus sign in front of the +x%5E2+ term
The maximum is midway between the 2 roots
To find the roots:
(1) +0+=+s%2A%28+144+-+2s+%29+
+s+=+0+
+144+-+2s+=+0+
+2s+=+144+
+s+=+72+
+%28+72+%2B+0+%29+%2F+2+=+36+
The maximum is at (s,A) = (36,A)
Now find +A+
+A+=+-2%2A36%5E2+%2B+144%2A36+
+A+=+-2592+%2B+5184+
+A+=+2592+
The maximum area is 2592 ft2
check answer:
Here's the plot:
+graph%28+400%2C+400%2C+-20%2C+80%2C+-200%2C+2800%2C+-2x%5E2+%2B+144x+%29+