Notice what prasum did. It is a procedure that works for every word problem.
First, name your variables in writing.
$width = W.$
$length = L.$
$perimeter = P.$
Second, take all the information that you are given explicitly in the problem or that you are implicitly expected to know and translate it into math speak in writing.
$P = W + L + W + L = 2W +2L.$
$P = 34.$
$L = W + 3.$
$Find\ value\ of\ L.$
Third, you now have a pure math problem; all the words are gone. Solve that problem.
$34 = P\ and\ P = 2W + 2L \implies 2W + 2L = 34.$
$L = W + 3 \implies 2L = 2(W + 3) = 2W + 6.$
$So\ 2W + (2W + 6) = 34 \implies 2W + 2W + 6 = 34 \implies 4W = 28 \implies W = 7 \implies L = 10.$
Fourth, check your answer.
7 + 3 = 10. Correct.
2 * 7 + 2 * 10 = 14 + 20 = 34. Correct.
If you remember to do these four steps for every word problem, you will soon find doing them correctly to be much easier.