Solving a Window Problem with Calculus

Date: 11/11/95 at 16:9:4
From: Anonymous
Subject: Norman window with isosceles triangle on top 

My question is just like the Norman window question, but I have an 
isosceles triangle on top.  Where do I start?  I seem to have 3 
unknowns. b, h and x.

 Help please.  

Date: 11/12/95 at 14:24:29
From: Doctor Ethan
Subject: Re: Norman window with isosceles triangle on top

Hello,

This is going to be a litle hard for me because I think that you
have not given me all the information that you have, but here we 
go.

   We have a window like this

             _
     /\       |
    /  \      |
   /    \     |h
  /      \    |
 /________\  _|
 |   b    |
 |        |
 |        |x
 |________|
     


I also am wondering if maybe it says that the window has a square 
on the bottom part.  If it does then b=x so that makes things a 
little simpler. If the bottom part isn't a square (and then b and 
x can be different) then check to see if they told you the ratio 
between b and h.  That would allow you to write one in terms of 
the other.(i.e. if they says b is half as long as h then b = 1/2 
h).

So then you can use your perimeter equation (write back if you 
need help figuring it out) to solve for one more variable, then 
plug those into the area equation.  You have an equation for area 
in terms of one variable, then to find the maximum area you can 
take the derivative and set it equal zero.

If this has made no sense then write back.  When you do, give me a 
few more specifics about what your question is.

-Doctor Ethan,  The Geometry Forum