SOLUTION: Find the length and the width of a rectangular garden for a horticultural designer who wants to enclose an area as large as possible with 500 feet of wires

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Question 575194: Find the length and the width of a rectangular garden for a horticultural designer who wants to enclose an area as large as possible with 500 feet of wires
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
This can be done without calculus.
I assume this is pre-calculus.
Let the sides be +x+, x+, +y+, and y
Let +A+ = area
+2x+%2B+2y+=+500+
+2y+=+500+-+2x+
+y+=+250+-+x+
+A+=+x%2A%28+250+-+x+%29+
+A+=+250x+-+x%5E2+
Because of the minus in front of the +x%5E2+ term,
this curve has a maximum and not a minimum.
The maximum occurs at x+=++-%28b%2F%282a%29%29+ when the
equation has the form +a%2Ax%5E2+%2B+b%2Ax+%2B+c+
+a+=+-1+
+b+=+250+
+-%28b%2F%282a%29%29+=+-%28+250%2F%282%2A%28-1%29%29%29+
x+=++125+
and
+y+=+250+-+x+
+y+=+250+-+125+
+y+=+125+
So the dimensions that maximize the area are A = 125 x 125
which is a square. ( This is always true when you are maximizing a
rectangular area )