MHB Formulas for Triangle Perimeter & Height

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The discussion focuses on deriving formulas for the minimum perimeter of a triangle when only the heights corresponding to sides a and b are known. Participants are asked to provide the maximum height and minimum height corresponding to side b, given the triangle's perimeter and the height corresponding to side a. Diagrams are encouraged to illustrate the concepts and calculations involved. The conversation emphasizes the mathematical relationships between triangle dimensions and their respective heights. Clear formulas and visual aids are sought to enhance understanding of these geometric principles.
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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Can you perhaps provide some diagrams and show what you've tried?
 

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