Optimization Problems

Question

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?

Answer 1

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?