Question

A particular map shows a scale of 1cm: 5km. What would the distance on a map be if the actual distance is 14km?

Answer 1

Hint: This question is from the topic geometry. In this question, we will find the scale on a map in cm if the actual distance is 14km. In solving this question, we will first find out the scale in the map for the actual distance as 1km. After that, we will find the scale on a map in cm for an actual distance of 14km. After solving the further question, we will get our answer.

Complete step by step solution:
Let us solve this question.
In this question, it is given that the map shows a scale of 1cm: 5km. That means if the scale of the map is 1cm, then on that scale the actual distance is 5km. So, using this scale we have to find the scale on a map if the actual distance is 14km.
We know that on a scale of 1cm, the actual distance is 5km.
Or, we can also say that
At An actual distance of 5km, the scale on the map is 1cm.
Now, we can say that
At An actual distance of 1km, the scale on the map is $${\displaystyle \frac{1}{5}}$$cm.
Similarly, we can say that
On actual distance of 14km, the scale on map is $$14\times {\displaystyle \frac{1}{5}}={\displaystyle \frac{14}{5}}=2.8$$cm
So, we get that the distance on the map will be 2.8cm if the actual distance is 14km.

Note: As we can see that this question is from the topic of geometry, so we should have a better knowledge in that topic. We can solve this question by an alternate method.
Method-2:
Scale=1cm: 5km
Or, we can say that
$${\displaystyle \frac{\text{Map distance}}{\text{Actual distance}}}={\displaystyle \frac{1\text{cm}}{5\text{km}}}$$
New actual distance is 14km.
Let the new map distance be x cm.
So, we can write
$${\displaystyle \frac{\text{New map distance}}{\text{New actual distance}}}={\displaystyle \frac{\text{xcm}}{\text{14km}}}={\displaystyle \frac{1\text{cm}}{5\text{km}}}$$
$$\Rightarrow {\displaystyle \frac{\text{xcm}}{\text{14km}}}={\displaystyle \frac{1\text{cm}}{5\text{km}}}$$
$$\Rightarrow {\displaystyle \frac{\text{x}}{\text{14}}}={\displaystyle \frac{1}{5}}$$
$$\Rightarrow \text{x}=14\times {\displaystyle \frac{1}{5}}=2.8$$
We get the new map distance as 2.8cm
So, map distance on actual distance of 14 km is 2.8cm