Answer:
A. incorrect; not the ratios of corresponding sides
Explanation:
You want to know if the proportion 4/12 = 12/x and its solution x=60 are correct for the given figure.
Corresponding sides
In the given figure, the side lengths, shortest-to-longest are ...
4, 8, 12
and
10, 20, x
The ratio 4/12 would match the ratio 10/x. The proportion shown in the problem statement is 4/12 = 12/x (not 10/x). Corresponding sides are not used.
The correct proportion would be ...
4/12 = 10/x ⇒ x = 30 . . . . . the solution x=60 in incorrect
Similarity
The vertical angles are congruent, and the marked angles are congruent, so the triangles are similar by the AA similarity postulate.
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Additional comment
The side lengths do not meet the requirements of the triangle inequality:
4 + 8 is not greater than 12
so these "triangles" are formed from segments whose lengths do not form a triangle.
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