It seems to be impossibly hard to make it so that when a TabStrip is in a container that the content area is able to fill the remaining space rather than fitting to the content. I have seen that there are work arounds for what appears to be the same issue for the jQuery KendoUI library but it looks like a hack rather than a true solution. (One shouldn't have to go to the code behind to make this happen). A simple "fillRemainingSpace" (or similar) would be perfect and have the TabStrip handle the rest. I expect this is pretty common scenario for anyone making application like UI websites.
As you can see from the image below the tab strip tabs can keep getting added and they do not care where the parent DIV or any other container ends. It would be appropriate for them to allow for scrolling if it goes outside the width of its container.
This is the way it is handled in jQuery
Like the SAPUI5 object page control, it is a tabstrip with horizontal orientation of the tab headers but vertical allignment of all tab sections within the tab content container. If the user clicks on one tab header, the tab content container will be scrolled down to the tab section linked to the tab header.
A preview is given in the link below.