SOLUTION: what is the least possible diagonal of a rectangle with a perimeter of 100

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Question 495663: what is the least possible diagonal of a rectangle with a perimeter of 100
Answer by richard1234(7193) About Me  (Show Source):
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If a and b are the side lengths with a+b = 50, we can find the minimum possible value of a diagonal several ways:

If you know power means, we have , equality occurs when a=b (square).
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The Cauchy-Schwarz inequality states that




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We can say that , the LHS is constant so we can maximize 2ab (twice the area of the rectangle) to minimize the diagonal d. We can show several ways the optimal case is a=b.
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All of these solutions yield as the minimal possible diagonal.