Question 84663
Let's give the room a length of n.
The width of the room is z.
The perimeter of the room would be n+z+n+z or 2n+2z.

We know that the width is 3 feet shorter than the length so we know that z=n-3.  
If we substitute that into the above perimeter formula we find that the perimeter equals 2n+2(n-3).  We know that the perimeter equals 62ft so we can say that
2n+2(n-3)=62
subtract 62 from each side
2n+2(n-3)-62=0
expand the brackets
2n+2n-6-62=0
simplify
4n-68=0
divide both sides by 4
4n/4-68/4=0/4
n-17=0
add seventeen to both sides
n=17

Now n is the length.  So we know the length is 17.
The width is n-3, so the width is 17-3 = 14.

Let's check that our answer is correct.
17+17+14+14=62.

Therefore length=17, width=14.