let

l = the length of the rectangle, l>0

w = the width of the rectangle, w>0

l > w

The area of a rectangular piece of cardboard is 90 square centimeters:

l*w = 90

and the perimeter is 46 centimeters:

2(l + w) = 46 divide both sides by 2

l + w = 23

l = 23 - w

plug l = 23 - w into l*w = 90:

(23 - w)*w = 90

by solving we find:

w = 5 cm

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

l = 23 - w

l = 23 - 5

l = 18 cm

the dimensions of the rectangle are: the length is 18 cm and width is 5 cm.