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Find the Maximum rectangular area that can be enclosed by a fence that is 224 m. Show your solution
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Let x be the length of the rectangle and y be its width.
Then x + y = = 112, and you are asked to find x and y in a way
to maximize the product x*y which is the area.
Express y via x: y = 112 - x, and substitute it into the product:
x*y = x*(112-x).
Now find the maximum of the quadratic function f(x) = x*(112-x) = .
The maximum is the vertex at x = :
x = = 56.
So, x = 56 feet. Then y = 112-x = 56 feet too, and the rectangle is actually a square.