Final answer:
Without the length of side OP, we cannot determine the measure of side PQ in similar triangles LMN and OPQ. The properties of similar triangles dictate that corresponding sides are proportional, but we need more information to solve for PQ.
Step-by-step explanation:
To solve for the measure of side PQ in similar triangles LMN and OPQ, we need to use the properties of similar triangles. In similar triangles, corresponding sides are in proportion. This means:
LM/MN = OP/PQ
Substituting the given lengths, we have 44/9.7 = OP/PQ. But because we don't have the length of OP, we cannot determine the length of PQ from this information alone. Also, please note there might have been an omission in the provided details since we need the length of the corresponding side in triangle OPQ to form a proportional equation.
If you have the length of side OP or a ratio of the sides of triangles LMN and OPQ, I would be able to provide the measure of side PQ.
Finally, let's correct a typographical error you might have seen! The formula for the perimeter of a rectangle should be P = 2l + 2w, where 'l' stands for length and 'w' stands for width. For the town square example with a length of 39.2 meters and width of 17.5 meters, the perimeter would be:
P = 2(39.2) + 2(17.5) = 78.4 + 35 = 113.4 meters.