RE: It's puzzle time again!
2022-07-08, 10:10 (This post was last modified: 2022-07-08, 10:24 by Milan Vančura.)
2022-07-08, 10:10 (This post was last modified: 2022-07-08, 10:24 by Milan Vančura.)
That's interesting question. Although the initial conditions are easy to formalize, they let to an eq. of degree 4 - or I'm missing something 
let set y=|DE| ; l=|BC| ; r=|CD|; S=26; V=36; T=8 - then:
L + R = S (evident)
R^2 + y^2 = T^2 (Pythagoras theorem)
y/R = L / V (similar triangles)
Another approach is to use analytic geometry: for each point C compute the eq. of bar bottom-right corner point- then, set the x coordinate of this point equal 26. Maybe I try this later but you might be faster
EDIT: This leads to eq. of degree 4 as well. Hmm, strange. Not only because of a need to solve such eq. but from physical POV as well: how we can tell why only one of those 4 solutions is real and other three not? Looks, I felt into a trap, I can see why this was announced as a puzzle now
let set y=|DE| ; l=|BC| ; r=|CD|; S=26; V=36; T=8 - then:
L + R = S (evident)
R^2 + y^2 = T^2 (Pythagoras theorem)
y/R = L / V (similar triangles)
Another approach is to use analytic geometry: for each point C compute the eq. of bar bottom-right corner point- then, set the x coordinate of this point equal 26. Maybe I try this later but you might be faster
EDIT: This leads to eq. of degree 4 as well. Hmm, strange. Not only because of a need to solve such eq. but from physical POV as well: how we can tell why only one of those 4 solutions is real and other three not? Looks, I felt into a trap, I can see why this was announced as a puzzle now