OT Trig Puzzle

[Bill Ballard]

At 12:36 AM +0100 10/31/03, Richard Brekne wrote:
>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 ?

It's a calculus problem (or resembles one I read in a calculus 
textbook), but that's not to say that I've got the numerical answer. 
But I started with your description (a rectangle with sides X and y):

x+x*(pie/2)+2y=10		which yields:

y=(10-2.5708*x)/2

I then took the product of these two to my computers graphing 
calculator, and got an inverted parabola. It looks as the the maximum 
product of these two occurs when x is slightly under 2. (Actually the 
graphing calculator yields the value at the apogee: x=1.94492, 
yielding y=7.5,minus a goat hair).

That's on the assumption that when x*y has its maximum value, 
(x*y)+(x/4)*pie will be as well.

But, hey! I'm with Barbie: "Math is hard." (I'm stepping aside for 
someone who has more than a high school diploma.)

Bill Ballard RPT
NH Chapter, P.T.G.

"I go, two plus like, three is pretty much totally five. Whatever"
     ...........The new math
+++++++++++++++++++++