Finding Maximum Area of Inscribed Rectangle in a Triangle Using Differentiation

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Discussion Overview

The discussion revolves around finding the maximum area of a rectangle inscribed within a triangle with given side lengths of 12, 16, and 20. The context includes calculus concepts, specifically differentiation, and the application of these concepts to solve a geometric problem.

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about how to begin solving the problem and seeks guidance on setting up the equation.
  • Another participant provides a link that may contain helpful information related to the problem.
  • A participant shares their personal experience of attending Georgia Tech and requests more direct assistance rather than general advice.
  • A later reply suggests a methodical approach, including drawing the triangle, labeling points, and establishing relationships between variables to express the area in terms of one variable before differentiating.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus on the best approach to solve the problem, with differing levels of understanding and requests for various types of assistance.

Contextual Notes

Some assumptions about the geometric relationships and the specific method of differentiation remain unaddressed, and the mathematical steps are not fully resolved.

theCandyman
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I recently had a calculus midterm, but was baffled at how to even start this question. Can anyone point me in the direction to start it? It deals with the maximum/minimum section using differentiation.

What is the maximum area of a rectangle inscribed within a triangle with sides 12, 16 and 20?
 
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That is so ironic, I go to Georgia Tech. Everyone here is always bashing UGA about being a school of dumb people. I appreciate it, but I was hoping for a more direct help, such as the set up for the equation. I know A = bh, but what do I take the deritive with respect to?
 
Last edited:
begin by drawing a picture. center the triangle on the xy plane. draw an arbitary inscribed rectangle and label the point where the triangle and rectangle meet as (x,y). you should also have a symmetric point labeled (-x,y). find relationship between y and x (using the length of the 3 sides of the triangle). express the area for the rect in terms of x, differentiate, set to zero, and solve.
 

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