Question

 One side of a rectangle is 20 cm larger than the other side. If you make the smaller side two times larger and the larger side three times larger, then the perimeter of the new rectangle would be 240 cm. Find the lengths of the sides of the original rectangle.

Answer 1

notice the picture below
whateve the length is, is 20 more than whatever the width is
so, the width is "w" units, so the length is w+20 units then

the perimeter is all lengths added, in this case length+length+width+width
or
2l + 2w which is the same as 2(w+20)+2w

now, the smaller side, width, if times 2
and the length, times 3
they give a perimeter of 240

so, one could say that 
$\bf \begin{cases} w=width\\ l=length\to w+20\\ p=perimeter\to 2l+2w\to 2(w+20)+2w\\ ---------------\\ p=240\qquad when\qquad 2w\qquad and\qquad 3l \\ \quad \\ 240=2(2w)+2(3l) \\ \quad \\ 240=2(w)+2[3(w+20)]\leftarrow \textit{solve for "w"} \end{cases}$

once you found "w", what is length? well, w+20