The scale of the map is 1/500000. Determine the distance on the ground if on the map they are 5 s and 22 cm.

The scale of the map is 1: 500000.
a) The distance on the map is 5 cm.
1. Let’s make the proportion:
1/500000 = 5 / x.
We use the main property of the “cross to cross” proportion: to find the unknown denominator of the second fraction (x), it is necessary to multiply the denominator of the first fraction (500000) by the numerator of the second fraction (5) and divide this product by the numerator of the first fraction (1). Thus:
x = 500000 * 5/1 = 500000 * 5 = 2500000 (cm).
2. Determine the distance on the ground in kilometers.
1 m contains 100 cm, then:
1 m = 100 cm;
x = 2500000 cm.
x = 2500000/100 = 25000 (m).
1 km contains 1000 m, then:
1 km = 1000 m;
x = 25000 m.
x = 25000/1000 = 25 (km).
Answer: the distance on the terrain, indicated on the map in scale 1: 500000 by a segment equal to 5 cm, is equal to 25 km.
b) a) The distance on the map is 22 cm.
1. Let’s make the proportion:
1/500000 = 22 / x.
We use the main property of the “cross to cross” proportion: to find the unknown denominator of the second fraction (x), it is necessary to multiply the denominator of the first fraction (500000) by the numerator of the second fraction (22) and divide this product by the numerator of the first fraction (1). Thus:
x = 500000 * 22/1 = 500000 * 22 = 11000000 (cm).
2. Determine the distance on the ground in kilometers.
1 m contains 100 cm, then:
1 m = 100 cm;
x = 11000000 cm.
x = 11000000/100 = 110000 (m).
1 km contains 1000 m, then:
1 km = 1000 m;
x = 110,000 m.
x = 110,000 / 1000 = 110 (km).
Answer: the distance on the terrain, marked on a map in scale 1: 500000 with a segment equal to 22 cm, is 110 km.