Final answer:
Due to an apparent typo mixing up squares with triangles, assuming the ratio given actually refers to the sides of a triangle, the length of the shortest side would be 18 meters, by finding the common factor in the ratio that corresponds to the total perimeter.
Step-by-step explanation:
The student's question seems to have a typo since squares have all sides of equal length, and thus the ratio given (3:5:17:11) isn't applicable. However, considering the actual question is likely about the sides of a triangle, given that there's mention of a perimeter, we can solve for the shortest side using the perimeter information. If the triangle's perimeter is 216 meters, and we assume that the ratio of the sides is a standard representation where all sides have a common factor, we can find this common factor and thus the length of the shortest side. Let's add the ratio numbers together: 3 + 5 + 17 + 11 = 36. This sum represents the total number of parts that make up the perimeter. We can then divide the perimeter by this sum to find the length of one part: 216 / 36 = 6 meters. Now we multiply the smallest ratio number (which is 3) by this length to find the shortest side: 3 * 6 = 18 meters. It's worth noting that for a square, the perimeter is calculated by P = 4 × side length, since all sides are equal. For triangles, there is no set formula for perimeter without knowing at least the lengths of the sides.