Question: A cartographer notes that 3.2 cm on a map corresponds to 16 km in reality, and 5.8 cm corresponds to $ x $ km. What is the value of $ x $?
["Title: Understanding Map Scale: How to Calculate Real Distances from Map Measurements", "When studying maps, one key detail cartographers emphasize is the scale — the relationship between distances on the map and actual distances on the ground. This scale allows users to accurately estimate real-world distances from map measurements.", "A recent observation by a professional cartographer illustrates this clearly. They noted that 3.2 cm on the map equals 16 km in reality. This ratio serves as the scale factor to convert any map measurement into real-world kilometers.", "### How to Use Map Scale for Real Distances", "Map scale is typically expressed as a ratio. In this case, the scale is:", "> 3.2 cm : 16 km", "To find the real distance corresponding to 5.8 cm on the map, follow these simple steps:", "1. Find the real distance per centimeter:\n Divide 16 km by 3.2 cm:\n $$\n \ ext{Scale factor} = \frac{16\ \ ext{km}}{3.2\ \ ext{cm}} = 5\ \ ext{km/cm}\n $$", "2. Multiply by the map distance:\n Multiply 5.8 cm by 5 km/cm:\n $$\n x = 5.8 \ imes 5 = 29\ \ ext{km}\n $$", "### Final Answer", "So, 5.8 cm on the map corresponds to 29 km in reality. Understanding this simple scaling method empowers anyone — from students to travelers — to interpret and utilize maps more accurately.", "Whether planning a hike, organizing a road trip, or studying geography, knowing how to convert map distances into real distances is an essential skill. Always check the map scale for precise measurements and ensure accurate navigation on the ground.", "---", "Key Terms: map scale, cartographer, real distance calculation, 3.2 cm = 16 km, How to convert map distances, geographic scaling, scalable map ratios."]
