let

w = the width of the rectangle, w>0

l = the length of the rectangle, l>0

P = 180 cm the perimeter of the rectangle

The width of a rectangle is two thirds the length:

w = (2/3)l

the perimeter = 2(length + width) that is P = 2(l + w) thus we have:

2(l + w) = 180 divide both sides by 2

l + w = 90

by solving the system of equations:

w = (2/3)l

l + w = 90

we find:

w = 36 cm

l = 54 cm

click here to see the step by step solution of the system of equations:

the dimensions of the rectangle are: the width is 36 cm and the length is 54 cm.