let

x = the length of the side of the first square

y = the length of the side of the second square

the side of one square is 3 cm longer than twice the side of the second square

x = 3 + 2y

the difference in their areas is 144 cm^2

x^2 - y^2 = 144

plug x = 3 + 2y into the last equation

(3 + 2y)^2 - y^2 = 144

by solving the equation we find and consider the positive roots (since the length of the side can not be a negative number)

y = 5 cm

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

Click to see all the steps

x = 3 + 2*5

x = 13 cm

the sides of the two squares are 5 cm and 13 cm.