Context: So I was working on finding the relationship between the variables in an isosceles triangular prism a,b(side lengths of rectangle and h (height of triangle). The problem is that I'm trying to find a general relationship between a,b,h so that I can use them to optimize the packaging of any isosceles triangular prism, for which I know the variables a,b,h, but I'm not sure how to continue. I'm using the bottom part of this thesis as a refference: https://www.clastify.com/ia/maths/5fba8e3bf4fda55746067a1b My working looks as follows:
I partially differentiated both equations then and used LaGrange's multipliers to set them equal to the constant lambda:
Next I set Eq. 1. a) and 3. a) equal to each other doing the same with 2. a) and 3.a) [wrongly annotated as 1. b) and 2. a)]
I then used symbolab to rewrite the Eq. in terms of b so that I can substitute the re-arranged Volume formula
