let

l = the length of the rectangle, l>0

w = the width of the rectangle, w>0

A = 90 cm^2 the area of the rectangle

The length of a rectangle is 3cm longer than twice the width:

l = w + 3

since the area A = length*width we have:

l*w = 90

plug l = w + 3 into the last equation:

(w + 3)w = 90

by solving we find:

w = 8.1 cm

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

l = w + 3

l = 8.1 + 3

l = 11.1 cm

the length of the rectangle is 11.1 cm.

the width of the rectangle is 8.1 cm.