I am having a calculus problem with a scenario where we move an object down a hall that is 8 feet wide and around a 90 degree corner to a hall that is 6 feet wide. I am hung up one aspect of the problem:

*I have to answer this - equations relating the independent variables from your formula and write the quantity to be maximized as a function of one variable.

I thought that I was on the right track but am not sure. I am attaching my work so far