Step 1: Understand the meaning of “Corpulent.”
“Corpulent” is an adjective describing someone who is large or overweight, usually referring to a person’s body size.
Step 2: Match with the synonym.
Among the given options, “Obese” directly means extremely overweight, making it the best match.
Step 3: Eliminate incorrect options.
- “Lean” means thin or slender—opposite meaning.
- “Gaunt” means extremely thin, usually from illness.
- “Emaciated” means abnormally thin or weak.
\[
\boxed{\text{(d) Obese}}
\]