# The distance between two points a and b on a map of scale 1: 2500000

**The distance between two points a and b on a map of scale 1: 2500000 = 12 cm. Find the true distance between these points on the surface of the earth.**

A map scale of 1: 2,500,000 shows that 1 cm on the map corresponds to 2,500,000 cm (25 km) at the surface of the earth. Let’s make a proportion: 1 cm = 2500000 cm; 12 cm = x. We use the main property of the “cross to cross” proportion: x = 12 * 2500000 = 30000000 (cm). Let’s convert 30,000,000 cm to meters. It is known that 1 m contains 100 cm, then: 1 m = 100 cm; x = 30,000,000 cm; x = 30000000/100 = 300000 (m). Let’s translate 300,000 m into kilometers. It is known that 1 km contains 1000 m, then: 1 km = 1000 m; x = 300000 m.x = 300000/1000 = 300 (km). Thus, the true distance between points a and b on the earth’s surface is 30,000,000 cm, or 300,000 m, 300 km.

Answer: 300 km.