How did inventions lead to an increase in Imperialism?

The Industrial Revolution led to imperialism in ways such as creating the demand for raw materials, which would be turned into products in factories, and providing the means to transport those raw materials with inventions such as the steam engine.

These new industrialized nations needed more raw materials to fuel their mass production and population growth. In order to maximize the countries profits, these industrialized nations went out to find nations that they could exploit natural resources and cheap labor from thus leading to imperialism.

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