Two towns , 17 km apart, are shown 3,4 cm on a map. What is the scale of the map, in its simplest form
3,4cm:17km = 1cm:5km = 1:500000
To find the scale of the map, we need to determine the ratio between the distance on the map and the corresponding distance in reality.
Given that two towns, which are 17 km apart in reality, are shown as a distance of 3.4 cm on the map, we can set up the following proportion:
Distance on the map / Distance in reality = Scale
Let's substitute the given values into the equation:
3.4 cm / 17 km = Scale
We need to convert the units of km to cm to match the units on the map:
1 km = 100,000 cm
17 km = 17 * 100,000 cm = 1,700,000 cm
Now we can calculate the scale:
3.4 cm / 1,700,000 cm = Scale
To simplify the scale ratio, we divide both the numerator and denominator by their greatest common divisor (GCD). The GCD of 3.4 and 1,700,000 is 0.1.
(3.4 cm ÷ 0.1) / (1,700,000 cm ÷ 0.1) = Scale
34 / 17,000,000 = Scale
The simplified scale of the map is 1:500,000.