For a given model of the ship, the height of the mast is 9 m, while the mast of the actual ship is 12 m high. If the height of the ship is 28 m, then the model is ____ meters high.

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For a given model of the ship, the height of the mast is 9 m, while the mast of the actual ship is 12 m high. If the height of the ship is 28 m, then the model is 21 meters high.Height of model ship’s mast = 9 m.Height of actual ship’s mast = 12 m.We have to find the height of the model ship’s mast if the height of the ship is 28 m.We know that if two quantities  and  vary in the same way while maintaining a constant ratio between their respective values, then the two quantities are said to be in direct proportion.i.e.

x
    y
   
   =k,
   where k is a constant positive number.As the height of the ship increases, the height of the mast also increases.Therefore, this is a case of direct proportion.So, we can arrange a table as given below:Actual ship’s mast height(m)

x
    1
   
   =12

x
    2
   
   =28
  Model ship’s mast height(m)

y
    1
   
   =9

y
    2
   
   =
  ?Using the relation of direct proportion

x
      1

y
      1

=

x
      2

y
      2

, we get,

x
      1

y
      1

=

x
      2

y
      2

⇒
    y
    2
   
   =

x
      2

y
      1

x
      1

⇒
    y
    2
   
   =
    
     28×9
    
     12

∴
    y
    2
   
   =21
    Therefore, the height of the model ship is 21 cm.

Actual ship’s mast height(m)	$x 1 = 12$	$x 2 = 28$
Model ship’s mast height(m)	$y 1 = 9$	$y 2 =$ ?

For a given model of the ship, the height of the mast is 9 m, while the mast of the actual ship is 12 m high. If the height of the ship is 28 m, then the model is ____ meters high.

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