let

l = the length of the original rectangle, l>o

w = the width of the original rectangle, w>0

a rectangle is three times as long as it is wide

l = 3w

if its length and width are both decreased by 2 cm, its area is decreased by 36 cm^2

l*w - (l - 2)(w - 2) = 36

plug l = 3w into the last equation

3w*w - (3w - 2)(w - 2) = 36

by solving we find

w = 5 cm

click here to see the step by step solution of the equation

l = 3*5

l = 15 cm

the original dimensions of the rectangle are 5 cm and 15 cm.