Let

l = the length of the room
w = the width of the room
P = 18 m is the perimeter

A rectangular room is 3 meters longer than it is wide:

l = w + 3

The perimeter is 18 meters:

P = 2(l + w)

2(l +w ) = 18 divide both sides by 2

l + w = 9

By solving the system of equations

l = w + 3
l + w = 9

we find

l = 6 m

w = 3 m

click here to see the step b y step solution of the system of equations

The room is 6 meters long and 3 meters wide.