Comparision of "Like" vs "As"

Hi! This is a very good question to ask. First of all, you correctly used 'like' in this context. Well done! If you had wanted to use 'as', it would've looked as follows: 'He runs as fast as a cheetah'. 

'like' is used when comparing nouns or pronouns, and will always be following by a pronoun or noun. Let's break down your example: 'He (pronoun) runs like a cheetah (noun).' - the pronoun 'He' is being compared to the noun 'a cheetah'. 

'as' is used to communicate that something is being done in the same manner as something else. Let's break down the example that I gave: 'He runs as fast as a cheetah.' - the manner in which he runs is being compared to the manner in which a cheetah runs. It's important to note that 'as' will be used twice when making the comparison. 

I hope that this helps you when making comparative sentences in the future.