To calculate the total length of the race course that goes around a triangle-shaped grassy area, we would need the lengths of the sides of the triangle. However, since only the provided options are available (17.31 km, 4.754 km, 5.754 km, 1.731 km), I will help you analyze them.
If you have the side lengths of the triangle, you could use them to find the total length by adding the lengths of all three sides. In case the side lengths aren’t provided and you have a diagram that shows the dimensions or a specific angle configuration, you could use that information to apply either the Pythagorean theorem (if it's a right triangle), Heron's formula (for generic triangles), or any other relevant geometric properties.
Please refer back to the diagram and calculate accordingly, or let me know if you have the side lengths. If this is based on a known configuration or formula, I'd be happy to help you with that as well!