Question

A model of an aeroplane is made to a scale 1:400. Calculate the length of the model in centimetre if the length of the aeroplane is 40metre.

Answer 1

Hint: Here, this can be solved by using the concept of similar triangles which is the same as that of ratio and proportionality i.e. ratio of corresponding sides are equal. So, here ratio 1:400 is given and can be considered as a ratio of two sides of the object. We have to find the length of the model in centimetre so, first convert the length of aeroplane from metre to centimetre using the conversion $1m=100cm$. Then using the concept $scale=\dfrac{\text{length of model}}{\text{length of aeroplane}}$ .

Complete step-by-step answer:
A ratio is the comparison or simplified form of two quantities of the same kind. It indicates how many times one quantity is equal to the other. It is expressed in the form of fraction.
Now, from the question we can collect data as scale $=1:400\Rightarrow \dfrac{1}{400}$ , length of model we can assume it as unknown variable ‘x’ and length of aeroplane $=40m$ .
First, converting metre to centimetre using the conversion $1m=100cm$ . So, applying unitary method, we get
$\begin{align}
  & 1m=100cm \\
 & 40m=? \\
\end{align}$
$\Rightarrow 40\times 100=4000cm$
Thus, the length of aeroplane is converted to centimetre.
Now, using the concept of a similar triangle which is the same as the ratio of taking two sides.
$\therefore scale=\dfrac{\text{length of model}}{\text{length of aeroplane}}$
Substituting the data we collected in above equation, we get
$\therefore \dfrac{1}{400}=\dfrac{x}{4000}$
On cross multiplying and making ‘x’ as subject, we get
$\Rightarrow x=\dfrac{1}{400}\times 4000$
$\Rightarrow x=10cm$
Thus, the length of the model obtained is 10cm.

Note: Students generally don’t understand which part will come in numerator and which in denominator. If we take ‘x’ in denominator and 4000cm in numerator then answer will be completely different, we get
$\therefore scale=\dfrac{\text{length of aeroplane}}{\text{length of model}}$
$\therefore \dfrac{1}{400}=\dfrac{4000}{x}\Rightarrow x=4000\times 400$
$x=1600000cm$
Thus, this above value is impossible in real life. So, it is a wrong calculation.