I'm revising for a cryptography exam at the moment and I'm having some problems with a question.

The question looks for the key length of a cipher given that the word "earthquake" appears in the plaintext.

Ciphertext: aaatr ksams itahb netrs weurs rheti aadne ttrht eakgt snqid s

I was wondering how I use the fact that the word "earthquake" appears in the plaintext to make it easier to obtain the key length?

At the moment, I'm just using the method of looking for repeated letters in the ciphertext to obtain a possible key length.

EDIT: Here's the actual question:

Consider the following ciphertext, [12 marks]

aaatr ksams itahb netrs weurs rheti aadne ttrht eakgt snqid s

i) Provide some evidence to suggest that this is not a substitution cipher.
ii) Determine the keylength of this cipher given that the word earthquake appears in the plaintext.
iii) Hence or otherwise decrypt this message to recover the plaintext.
iv) Historically a variant of this cipher had a very important application. Briefly describe the variant and the application.