What did people feel they need in the middle ages due to the absence of the Roman Empire?

Political structure and strong regulations

Explanation:

During the reign of roman empire, many of the smaller regions across Europe followed the rules/regulations imposed by the Roman empire. In exchange for giving their loyalty to the Roman empire, they received protection from Roman soldiers every time criminal activities arise in their community.

After the fell of roman empire, these regions did not really have any laws that they should adhere to.  As a result, many of these regions started to turn into chaos. The people are openly killing/stealing within their communities and there's also another threat from barbarians(outsiders) who saw an opportunity to attack in absence of Roman soldiers.

the perimeter of a triangle is 69 cm. side a is 5 cm shorter than side b. side c is twice as long as side a. find the length of each side. i need to know how to do it in 2 equations.  

equations:

a = b-5

c = 2a

a + b + c = 69

bujías y una hora antes y no me parece muy difícil