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Given different continuous ranges of values for the legs, how can I find the values that maximize the length pf the hypotenuse of the right triangle? In other words, given that A lies between X and Y and B lies between C and D, how can I find the values that result in the highest possible value of sqrt (c^2)?

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You want to maximize the function $\;f(a,b):=\sqrt{a^2+b^2}\;$ given that $\;a\in[X,Y]\;,\;\;b\in[C,D]\;$ . But it's easy to see this happens when $\;a=\max\{|X|,|Y|\}\,,\,b=\max\{|C|,|D|\}\;$ as we have a sum of squares within that square root...

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  • $\begingroup$ so you're saying that it's again just the maximum values of the range? $\endgroup$ – Joe Stavitsky Feb 10 '14 at 16:07
  • $\begingroup$ Isn't that obvious, @JoeStavitsky ? I mean, the square root function is an ascending one... $\endgroup$ – DonAntonio Feb 10 '14 at 16:12

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