Question

The linear scale of a map is $1cm=2m$ . The drawing dimensions of an on – site rectangular plot measuring $25m\times 40m$ will be:
A.$50cm\times 80cm$
B.$25cm\times 40cm$
C.$12.5cm\times 20cm$
D. $5cm\times 8cm$

Answer 1

Hint: Whenever we are required to do the scaling, mostly the scaling will be done from one unit to the other. The size of the things matters a lot in this case.

Complete step-by-step answer:
When we are scaling, we are either scaling from bigger units to the smaller ones, or we are scaling smaller units to bigger ones. In other words, we are either zooming in or zooming out of the object under consideration.
This thing is used in our daily life, without us even noticing to this, like whenever we are travelling and using maps on our phones, we would like to zoom in and the look closely how the actual path is looking or whenever we are drawing a sketch, we sometimes stop and measure the comparable objects around and draw accordingly for more accuracy.
In our question, we need to scale up, i.e. we are zooming out. We are given that the linear scale of a map is $1cm=2m$ .
Therefore, $1m=\dfrac{1}{2}cm$ .
Hence, for drawing dimensions of an on – site rectangular plot whose dimensions are $25m\times 40m$ we will be using our linear scale for this scaling.
Since, $1m=\dfrac{1}{2}cm$ $-\left( 1 \right)$
Therefore, multiplying $-\left( 1 \right)$ by $25$ , we get:
$1\times 25m=\dfrac{25}{2}cm$
$\Rightarrow 25m=12.5cm$ .
And, multiplying $-\left( 1 \right)$ by $40$ , we get:
$1\times 40m=\dfrac{40}{2}cm$
$\Rightarrow 40m=20cm$ .
Hence, the drawing dimensions of the required plot will be $12.5cm\times 20cm$ .
Hence, option C. $12.5cm\times 20cm$ is the correct option.

Note: Whenever we will be scaling, a special attention on the units must be given as if we write the things the other way round, the whole thing will be wrong. Also, we can always look upon options if there is only one option of the required units, we can directly choose that option without even calculating the things.