Question

The scale of a map is $$1:250000$$.
(a) The actual distance between two cities is 180 km.
(b) Calculate this distance on the map. Give your answer in centimeters.

Answer 1

Hint: Here, we will find the scale of the given representative fraction and then find the distance of the two cities on the map. If the answer is not in centimeters, then we will convert the answer in centimeters.

Complete step-by-step solution:
Given that the representative fraction is $$1/250000$$.

We know that the representative fraction is the ratio of map distance to the corresponding ground distance is independent of units of measurement.

This implies that 1 cm on the map is actually 250000 cm distance.

First, we will convert this 250000 cm into m as $$1\text{ m}=100\text{ cm}$$.

$$250000\times {\displaystyle \frac{1}{100}}\text{ m}=2500\text{ m}$$

Now we will convert this into km as $$1\text{ km}=1000\text{ m}$$.

$$2500\times {\displaystyle \frac{1}{1000}}\text{ km}=2.5\text{ km}$$

So, 1 cm on the map is $$2.5\text{ km}$$ actual distance.

Now, we will find the distance on the map corresponding to 180 km on ground.

$$\begin{gathered} {\displaystyle \frac{180}{2.5}}\text{ cm}={\displaystyle \frac{1800}{25}}\text{ cm} \\ =72\text{ cm} \end{gathered}$$

Hence, the two cities are 72 cm apart on the map.

Note: In this question, we are supposed to scale the representative fraction properly to avoid any miscalculation. Also, we will take care of the scales properly i.e. kilometers, meters and centimeters.