MHB Maxima and minima of a triangle

AI Thread Summary
The discussion revolves around deriving formulas for specific triangle properties. The first query seeks the minimum perimeter of a triangle given the heights corresponding to sides a and b. The second question asks for the maximum height and minimum height corresponding to side b, based solely on the perimeter and height of side a. Participants clarify the need for precise mathematical expressions to address these inquiries. The conversation emphasizes the importance of understanding triangle geometry for accurate calculations.
loquetedigo
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Write the following formulas:

a) The minimum perimeter of any triangle (abc) only known heights corresponding to the sides a and b.

b) The maximum height and minimum corresponding to the side b of any triangle (abc) only known the value of its perimeter and height corresponding to the side a.
 
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Adrian,

I could be wrong, but I think the OP mistakenly posted a question with which they want help here. :)
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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