If the length of the rectangle is twice the width and the perimeter of the rectangle is 30 cm find its area

Lets let width=x meters. 
Length is twice the width, twice meaning two times and we know that the width is x so length = 2x. 
The perimeter is the sum of all the sides or width + width + length + length which is equal to x + x + 2x + 2x by substituting x for width and 2x for length. We know that x is really 1x since 1 times anything is that anything. 
So the perimeter can be written as 1x + 1x + 2x + 2x which we are told is equally 42 meters. We reduce the equation by collecting all terms that have the same variables so we get (1 + 1 + 2 + 2 )x = 42. Adding the collected terms together we get 6x = 42. Now we solve for x by dividing both sides of the equation by six. Whatever we do to one side we have to do to the other so the equation remains balanced. So 6x divide by 6 is 1x or we can just say x, and 42 is divided 6 giving us 7. So x = 7. Going back to our original stated facts width = x = 7 and length = twice the width or 2x = 2 (7) =14. So 
width = 7 meters 
legth = 14 meters 

We can double check this since we know the formular for the perimeter = width + width + length + length = 7 + 7 + 14 + 14 = 42.