SOLUTION: What happens if the base of the rectangle is 0? Do you obtain a realistic value of the area? Explain. Explain why the graph is symmetric. a. Give an explanation for why

Question 384976: What happens if the base of the rectangle is 0?
Do you obtain a realistic value of the area? Explain.
Explain why the graph is symmetric.
a. Give an explanation for why there is only one data point for the largest area.
b. What do you notice about that data point and the rectangle?

Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
If the base of a rectangle is 0, the rectangle is degenerate and has zero area.
For a given perimeter, if the side lengths are x and c-x, the graph is symmetric because the area is a quadratic in terms of x. It is maximized when x = c-x, i.e. the rectangle is a square. This is because quadratic equations have only one vertex.
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