Here is what we know
W=width
L=Length
P=Perimeter
2l+2W=P
2l+2W=164
l+62=w
Solve the bottom equation for l by subtracting 62
l=w-62
Plug the value for l back in to 2l+2W=164
2(w-62)+2w=164
distribute the 2
2w-124+2w=164
simplify by adding the w terms
4w-124=164
add 124 to both sides
4w=288
divide both sides by 4
w=72
Plug w back into 2l+2w=164
2l+2(72)=164
2l+144=164
subtract 144 from both sides
2l=20
divide both sides by 2
l=10
that means that 10+10+72+72 should equal 164. If you add those up you will find that they do.
Length=10
Width=72