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MatinSAR
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This is better.Hill said:
Thank you one more time for your help.Hill said:
Find the sides of the right triangle so that their sum is minimized
- Thread starter MatinSAR
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SUMMARY
The discussion centers on finding the sides of a right triangle that minimize the sum of the legs \(a + b\) given a fixed hypotenuse \(c = 5\). The mathematical approach involves using the Pythagorean theorem \(a^2 + b^2 = c^2\) and calculus to derive that \(a = \frac{c}{\sqrt{2}} \approx 3.54\) and \(b = \frac{c}{\sqrt{2}} \approx 3.54\) yield a maximum sum of approximately 7.07. However, the minimum sum occurs when either \(a\) or \(b\) approaches zero, resulting in a sum of 5, which is not feasible for a triangle. The conclusion is that there is no valid minimum for \(a + b\) under the constraints of triangle geometry.
PREREQUISITES- Understanding of the Pythagorean theorem
- Basic calculus, specifically differentiation
- Knowledge of constraints in optimization problems
- Familiarity with triangle properties and definitions
- Study the implications of constraints in optimization problems
- Explore the concept of limits and their application in calculus
- Learn about integer solutions in Pythagorean triples
- Investigate the taxicab metric and its applications in geometry
Mathematicians, students studying geometry and calculus, educators teaching optimization problems, and anyone interested in the properties of triangles and their applications in real-world scenarios.
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