The following sentence has been divided into four segments. Identify the segment that contains an adverbial usage error.
Mrs. Gomathi was / that tired and weak / that she could / scarcely walk.

The correct option containing an adverbial usage error is "that tired and weak".

Detailed Explanation:

In English grammar, when expressing a cause and effect relationship where an intensity of a quality leads to a specific result, the structure "so... that" is used.

Here, the adjective phrase "tired and weak" describes the condition of Mrs. Gomathi, and the clause "that she could scarcely walk" expresses the result of her condition. To modify the adjectives "tired and weak" to show the degree causing this result, the adverb "so" should be used instead of "that".

Correct Structure:

Subject + verb + so + adjective/adverb + that-clause

Corrected Sentence:

"Mrs. Gomathi was so tired and weak that she could scarcely walk."

Therefore, the segment "that tired and weak" contains the adverbial error.