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 > _______________________________________________ > pianotech list info: https://www.moypiano.com/resources/#archives
This PTG archive page provided courtesy of Moy Piano Service, LLC