OT Trig Puzzle

[David Love]

The area will be maximized when the rectangle has equal sides (remember all
squares are rectangles even though all rectangles are not squares).  Thus:

All sides of the rectangle can be represented by "x".

The perimeter of the figure is:

(pi*x)/2 + 3x = 10

multiply each side by 2

pi*x + 6x = 20

factor out an x from the left side

x(pi + 6) = 20

multiply each side by 1/(pi + 6)

x = 20/(pi + 6)

solve 

x = 2.187803  approximately. 

That's my guess.   

David Love
davidlovepianos@earthlink.net


> [Original Message]
> From: Richard Brekne <Richard.Brekne@grieg.uib.no>
> To: Newtonburg <pianotech@ptg.org>
> Date: 10/30/2003 5:36:34 PM
> Subject: OT Trig Puzzle
>
> Ok guys and gals... so you think you remember you High School Trig eh ??
>
> Here is a refresher problem
>
> A half circle is placed on top of a rectangle such that its diameter is
> the top side of the rectangle. The length of the 3 remaining sides of
> the rectangle, plus the circumference of the half circle is equal to 10
> cm.
>
> Question: What are the lengths of the sides of the rectangle when the
> area of the combined figure is at its maximum ?
>
>
> ... just in case you are bored with your weekend :)
>
> Cheers
> RicB
>
> -- 
> Richard Brekne
> RPT, N.P.T.F.
> UiB, Bergen, Norway
> mailto:rbrekne@broadpark.no
> http://home.broadpark.no/~rbrekne/ricmain.html
> http://www.hf.uib.no/grieg/personer/cv_RB.html
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