Final answer:
The lateral decubitus position is best for radiographically demonstrating intestinal perforation, as it allows detection of free gas within the peritoneal cavity, indicating the presence of perforation.
Step-by-step explanation:
The radiographic position that best demonstrates perforation of the intestines is the lateral decubitus position. This position is particularly useful for detecting free air or gas that has escaped from a perforated bowel, as it allows the air or gas to rise and become visible in the area of the peritoneal cavity, between the visceral peritoneum which covers the organs, and the parietal peritoneum which lines the abdominal wall.
The lateral decubitus position involves the patient lying on their side, which can cause any free air present to rise to the highest point in the abdominal cavity, usually near the liver when the patient is lying on the left side, making it visible on an X-Ray. This is indicative of intestinal perforation and requires immediate medical attention.