let

h = the height of the parallelogram,a >0

a = the length of the base, h>0

A = 135 mm^2 the area of the parallelogram

the ratio of the height of a parallelogram to its base is 3:5:

h : a = 3 : 5 cross-multiply

5h = 3a divide both sides by 5

h = (3/5)a

the formula for the area of a parallelogram is: A = (1/2)ah thus we have

(1/2)ah = 135

plug h = (3/5)a into the last equation:

(1/2)a(3/5)a = 135

by solving we find:

a = 21.21 mm approximately

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

the length of the base is 21.21 mm.