A 2.5 cm segment on the map corresponds to a distance of 12.5 km on the ground. a) What is the scale of this map?

A 2.5 cm segment on the map corresponds to a distance of 12.5 km on the ground. a) What is the scale of this map? b) What is the distance between two cities on the ground, if it is depicted on the map as a segment with a length of 5.1 s?

1. Let’s find the scale of the map, if the length of the segment shown on the map is 2.5 cm. And the distance in reality, on the ground, this segment length corresponds to 12.5 km:

1 cm = 100,000 km;

2.5 – 1

1250000 – x;

x = 500000

The scale is 1: 500000;

2. Let’s find the distance between two cities on the ground, if the distance on the map between these cities is shown by a segment of 5.1 cm. Let’s compose and solve the proportion:

5.1 – 1

x – 500,000;

x = 5.1 * 500,000 / 1 = 2,550,000 cm;

2,550,000 / 100,000 = 25.5 km;

Answer: the real distance between cities is 25.5 km.