Final answer:
Upon calculating based on the given relationship and perimeter, the length of side HG should be 27 units, but this answer is not among the provided choices.
Issue in the options.
Step-by-step explanation:
In parallelogram EFGH, side EF is three times larger than side FG, and the perimeter is 72 units. To find the length of side HG, we need to start by setting up the relationship given: EF = 3FG. Since opposite sides of a parallelogram are equal in length, we have EF = HG and FG = EH. Therefore, the perimeter (P) of the parallelogram can be expressed as P = 2EF + 2FG. Given that the perimeter is 72 units, we can replace P with 72 and EF with 3FG to get the equation 72 = 2(3FG) + 2FG, which simplifies to 72 = 6FG + 2FG, and further to 72 = 8FG. Dividing both sides of the equation by 8, we find FG = 9 units. Since EF = 3FG, we can calculate the length of EF (which is the same as the length of HG) as EF = 3 × 9 units = 27 units. However, this is not an option in the multiple-choice answers given. The mistake could be in the initial setup of the problem or in the options provided.