SOLUTION: a rectangular storage area is to be constructed along the side of tall building, a security fence is required along the remaning three sides of the area. what is the maximum

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Question 164437: a rectangular storage area is to be constructed along the side of tall building, a security fence is required along the remaning three sides of the area. what is the maximum area that can be enclosed with 800 ft of fencing.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the side parallel to the building x ft
Then the remaining 2 sides would each be
%28800+-+x%29%2F2 ft
The area can then be expressed as
A+=+x%2A%28800+-+x%29%2F2
A+=+%28800x+-+x%5E2%29+%2F+2
A+=+400x+-+x%5E2%2F2
This is a parabola which, because the coefficient of
x%5E2 is negative, has a maximum and not a minimum
The maximum is at -%28b%2F2a%29
a+=+-%281%2F2%29
b+=+400
-%28b%2F2a%29+=+-%28400%2F-1%29
-%28400%29%2F-1+=+400
The maximum area is 400 ft2
I'll check by finding x
A+=+400x+-+x%5E2%2F2
400+=+400x+-+x%5E2%2F2
-x%5E2%2F2+%2B+400x+-+400+=+0
-x%5E2+%2B+800x+-+800+=+0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+-1
b+=+800
c+=+-800
x+=+%28-800+%2B-+sqrt%28+800%5E2-4%2A%28-1%29%2A%28-800%29+%29%29%2F%282%2A%28-1%29%29+
x+=+%28-800+%2B-+sqrt%28+640000+-+3200+%29%29%2F-2%29+
x+=+%28-800+%2B-+sqrt%28+636800+%29%29%2F-2%29+
x+=+%28-800+%2B-+797.997%29%2F-2%29+
If I use the (+) value of the square root, I get too small a value
for x, so I'll use the (-) square root
x+=+-1597.997%2F-2
x+=+798.998
The remaining sides are
1.002%2F2+-+.501each
A+=+798.998%2A.501
A+=+400.297 The error is due to rounding off, I think