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Optimization Problems

6 segments of a window frame are to be constructed from a piece of window framing material 6 m in length. A carpenter wants to build a frame for a rural gothic style window, where the triangle ABC is equilateral. The diagram looks like a house, an equilateral triangle labeled ABC and a rectangle below that is connected to BC. What should the dimensions be?

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Robert A. | Certified Teacher and Engineer - Tutoring Physics, Maths, and SciencesCertified Teacher and Engineer - Tutorin...
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Call the two sides of the window H for height. Call the top and bottom W for width.
Given the top light is an equilateral triangle, all three sides are equal,
and given the base forms the top width of the window; the sides must also = W.
So we have  (2 x H) + (4 x W) = 6 meters.
I have 2 unknowns and only 1 equation so if I understand the question correctly,
we are missing a set of constraints that will give us a second equation.
Is there more to it you might have missed in the problem?


p.s. I said "top light".  In case you are not familiar with the term,
each pane of glass in a window is called a light.