MHB Maxima and minima of a triangle

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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 'Area of Overlapping Squares'

Here is a little puzzle from the book 100 Geometric Games by Pierre Berloquin. The side of a small square is one meter long and the side of a larger square one and a half meters long. One vertex of the large square is at the center of the small square. The side of the large square cuts two sides of the small square into one- third parts and two-thirds parts. What is the area where the squares overlap?
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