Find the sides of the right triangle so that their sum is minimized

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Homework Help Overview

The discussion revolves around finding the sides of a right triangle such that their sum is minimized, given the relationship defined by the Pythagorean theorem, \(a^2 + b^2 = c^2\). Participants explore the implications of constraints on the values of \(a\) and \(b\) based on a fixed hypotenuse \(c\).

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the mathematical approach to minimizing \(a + b\) while adhering to the constraint \(a^2 + b^2 = c^2\). Questions arise regarding the nature of constraints and the validity of certain values for \(a\) and \(b\), particularly when considering lengths that approach zero.

Discussion Status

The discussion is ongoing, with various interpretations of the problem being explored. Some participants suggest that there is no minimum for \(a + b\) under the given constraints, while others question the validity of specific values proposed for \(a\) and \(b\). There is a recognition of the need for clarity regarding the constraints of the problem.

Contextual Notes

Participants note that the lengths of the sides must be positive and less than the hypotenuse, leading to a debate about the implications of approaching zero length. The original problem statement is also questioned for its clarity and correctness.

  • #31
Hill said:
What would be enough is assuming that North-South directions and East-West directions are mutually orthogonal everywhere in the area in question.
This is better.
Hill said:
If one starts at any point on that map and goes South, he follows a ray which goes from the North Pole and passes through the starting point.
If he goes East or West, he follows a circle which has its center at The North Pole and which passes through the starting point.
Thank you one more time for your help.
 
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  • #32
MatinSAR said:
It's not enough for the question you mentioned, But I guess it's enough to solve the main question which is related to high school. Do you agree? He doesn't walk that much(only 5 km) so the question doesn't want us to consider that he is walking on a sphere and ...
It does not really matter that @Hill disagrees.

The given problem, as you eventually stated in post #9, is quite clear. Your recent replies to @FactChecker reinforce that the given problem refers to 2D grid on a planar surface.
 
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  • #33
SammyS said:
It does not really matter that @Hill disagrees.

The given problem, as you eventually stated in post #9, is quite clear. Your recent replies to @FactChecker reinforce that the given problem refers to 2D grid on a planar surface.
Thank you @SammyS for your help.

Thank you to everyone who helped for his time.
 

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