Calculus optimization problem

  • Thread starter thegame
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  • #1
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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
 

Answers and Replies

  • #2
1,036
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Is there a question here?
 
  • #3
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How do you ge the answer?
 
  • #4
1,036
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How did YOU get the answer?
 
  • #5
Hurkyl
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Well, if you know one side of a rectangle inscribed in a semicircle, can you figure out the other side?
 
  • #6
1,036
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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 lets 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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