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

Given,

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

By formula,

⇒ Length of model = k × Length of object

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

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

By formula,

⇒ Breadth of model = k × Breadth of object

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

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

Hence, Option 2 is the correct option.