MHB Is the perimeter numerically equal to the area in this equation?

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The discussion focuses on proving that (1/2)uv equals u + v + w, where u, v, and w are defined in terms of variables m and n. The approach suggested involves substituting the values of u, v, and w into the equation and verifying that both sides are equal. It is noted that an indirect method, starting from the final equation and working backward, may be more effective for this proof. The importance of ensuring that each step is reversible is emphasized to validate the proof. The question is acknowledged as interesting, and further exploration is anticipated.
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If u = 2(m + n)/n, and v = 4m/(m - n), and

w = 2(m^2 + n^2)/(m - n)n, show that

(1/2)uv = u + v + w (that is, the perimeter is numerically equal to the area).

This question is basically a plug and chug situation.
I must multiply (1/2) by the given values of u and v on the left side. I must then replace u, v and w on the right side with their given values and add. The right side must = the left side, right?
 
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Yes, it looks like the simplest way to do this is NOT "directly", starting from the given values of u, v, and w and then showing the final equation, but "indirectly", starting from the final equation then working to the equations for u, v, and w. As long as every step is "reversible", that will prove what you want.
 
I will work this out when time allows. Interesting question.
 

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