What Is the Area of the Largest Rectangle Inscribed in a Semicircle?

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Homework Help Overview

The discussion revolves around determining the area of the largest rectangle that can be inscribed within a semicircle of radius r. Participants are exploring the geometric relationships and mathematical reasoning involved in this problem.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants are questioning the derivation of the area and the relationships between the sides of the rectangle and the semicircle. There is an emphasis on finding a way to express one dimension in terms of the other.

Discussion Status

The discussion is active, with participants seeking clarification on the initial answer provided and exploring how to derive the dimensions of the rectangle. Some guidance has been offered regarding the geometric setup and relationships, but no consensus has been reached.

Contextual Notes

There appears to be some confusion regarding the initial answer and the method to arrive at it, indicating that assumptions about the problem setup may need to be clarified.

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What is the area of the largest rectangle that can be inscribes indiside a semicircle with the radius r?

answer: x = r / SQRT(2)
A = r^2
 
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Is there a question here?
 
How do you ge the answer?
 
How did YOU get the answer?
 
Well, if you know one side of a rectangle inscribed in a semicircle, can you figure out the other side?
 
What Hurkyl's getting at is:

Draw the semicircle. Draw a rectangle inside it, call one side h, call the other side w, call the radius r.

Now find a relationship that let's you eliminate either h or w. In other words, express h as a function of w, or w as a function of h.
 

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