Question

The distance between city A and B on a map is given as \[6\ \]cm, if the scale represents $1\ \text{cm}=200\ \text{km}$ then find the actual distance between city A and city B in meters.

Answer 1

Hint:
For solving this question first we have to find the distance in km from the given data in question then we have to convert distance obtained in km into meters by multiplying the obtained distance with $1000$. By solving this we have the distance in meters between two cities.

Complete step by step solution:
We have the question to find out the distance between city A and city B in meters.
Given that
The distance between city A and B on a map is $=6\ \text{cm}$
While we are converting scale into distance it is given that
$1\ \text{cm}=200\ \text{km}$
Therefore, the total distance between city A and city B is given by
$d=6\left( 200\ \text{km} \right)$
$\Rightarrow d=1200\ \text{km}$
This is the distance between city A and city B in km. Now we have to find out the distance in meters. For that we have to convert km into meters.
We know that
$1\ \text{km}=1000\ \text{m}$
Therefore, the distance between city A and city B is
$d=\left( 1200\times 1000 \right)\ \text{m}$
$\Rightarrow d=12\times {{10}^{5}}\ \text{m}$
Therefore, the distance between city A and city B in meters is
$d=12\times {{10}^{5}}\ \text{m}$

Additional information:
A meter or meter is the base unit of length and distance in the International System of Units (SI). The meter is defined as the distance traveled by light in a second. It is denoted as cm.

Note:
For solving these types of questions it is very important to first convert the distance given in the map into km. Kilometer is an entity of length in the International System of Units (SI), the current form of the metric system. It is defined as $1000 $ meters.