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Mathematics

The length and the breadth of the model of a rectangular object are 12 cm and 7 cm respectively. If the scale factor is 1 : 20, the actual length and breadth of object are :

  1. 1 m & 20 m

  2. 2.4 m & 1.4 m

  3. 12 cm & 140 cm

  4. 1.2 m & 0.7 m

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Answer

Given,

Scale factor (k) = 1 : 20 or 120\dfrac{1}{20}

By formula,

⇒ Length of model = k × Length of object

⇒ Length of object = 1k\dfrac{1}{k} × Length of model

⇒ Length of object = 1120×12\dfrac{1}{\dfrac{1}{20}} \times 12 = 20 × 12 = 240 cm = 240100\dfrac{240}{100} = 2.4 m.

By formula,

⇒ Breadth of model = k × Breadth of object

⇒ Breadth of object = 1k\dfrac{1}{k} × Breadth of model

⇒ Breadth of object = 1120×7\dfrac{1}{\dfrac{1}{20}} \times 7 = 20 × 7 = 140 cm = 140100\dfrac{140}{100} = 1.4 m.

Hence, Option 2 is the correct option.

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