Question

In a ship of length 28m, the height of its mast is 12m. If the height of the mast in its model is 9cm what is the length (in cm) of the model ship?

Answer 1

Hint- To solve this problem convert all the given length in the same unit. Then take the ratio of height of original mast to the height of mast in its model and equate this ratio with the ratio of length of ship to the length of ship in its model.


Complete step by step solution:
In this question it is given that
The height of its mast is 12m
On converting the length from meter to centimetre
We get
\[ = 12 \times 100\;\]cm\[ = 1200\;\] cm
height of the mast in its model is 9cm
now find the ratio of height of mast in its model to the height of mast in original
So, ratio = height of mast in model / height of the mast in original
\[\; = \dfrac{9}{{1200}}\]
So, height in the model decreases by this ratio.

This same ratio will be there for length of ship and its length in model
Converting the given length of ship in meter to centimeter
length of original ship =28 m
=28×100=2800
\[ = 28 \times 100\]
\[ = 2800\;\]cm
Now equating the ratios
We get,
So, length of ship in the model / length of original ship = ratio
length of ship in the model = ratio x length of original ship
on putting the values we get,
\[ = \dfrac{9}{{1200}} \times 2800{\text{ }}\]
\[ = \dfrac{{9}}{3} \times 7\]
\[ = 21\;\] cm
Hence we find the length of the ship in the model is equal to 21 cm.

Note: Before solving these type of problems,always ensure that all the quantities are expressed in the sam unit and then the values are substituted.Do not substitute the values directly without converting them into a standard unit