Answer:
Here are some possible corrections for the run-on sentence:
The cucumber is an acidic vegetable. It has been around for more than 4,000 years.
OR
The cucumber is an acidic vegetable; it has been around for more than 4,000 years.
OR
The cucumber, an acidic vegetable, has been around for more than 4,000 years.
OR
The cucumber is an acidic vegetable that has been around for more than 4,000 years.
OR
The cucumber is an acidic, 4,000-year-old vegetable.