MHB Formulas for Triangle Perimeter & Height

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SUMMARY

The discussion focuses on deriving specific formulas related to triangle geometry. The minimum perimeter of a triangle with known heights corresponding to sides 'a' and 'b' is established through geometric principles. Additionally, the maximum height and minimum corresponding to side 'b' are determined based on a given perimeter and the height corresponding to side 'a'. Diagrams and examples were requested to illustrate these concepts effectively.

PREREQUISITES
  • Understanding of basic triangle properties and terminology
  • Familiarity with geometric formulas related to perimeter and height
  • Knowledge of trigonometric relationships in triangles
  • Ability to interpret and create geometric diagrams
NEXT STEPS
  • Research the derivation of triangle perimeter formulas
  • Study the relationship between triangle height and side lengths
  • Explore geometric proofs involving minimum and maximum values in triangles
  • Learn how to create and interpret geometric diagrams for triangle properties
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Mathematicians, geometry students, educators, and anyone interested in advanced triangle properties and geometric 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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Can you perhaps provide some diagrams and show what you've tried?
 

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