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| Math Central | Quandaries & Queries |
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Question from Christy, a student: Show that among all rectangles with an 8m perimeter, the one with the largest area is a square. I know this is simple but I'm not sure if I'm doing it correctly. Here is what I did. 1. A = xy Not sure what to do from this point because I don't know if its right. Christy |
Christy,
What you have done so far is correct. What you do next depends on what you know. Is this a calculus problem? If so the differentiate the function A(x) = 4x - x2 and solve A'(x) = 0 to find any critical points. This gives x = 2 and what remains is to show that x = 2 actually yields a maximum.
If this is not a calculus class then you might have an expression that tells you where the maximum or minimum of a parabola appears. You might notice that the parabola A = x(x - 4) crosses the x-axis at x = 0 and x = 4 and then conclude by the symmetry of the parabola that the maximum must appear half way between 0x = 0 and x = 4.
If this doesn't help then write back.
Harley
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