Question

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 the object are ______.

Options

• 1 m & 20 m

• 2.4 m & 1.4 m

• 12 cm & 140 cm

• 1.2 m & 0.7 m

Answer 1

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 the object are 2.4 m & 1.4 m.

Explanation: 

Given,

Scale factor (k) = 1 : 20 or `1/20`

By formula,

⇒ Length of model = k × Length of object

⇒ Length of object = `1/k`​ × Length of model

⇒ Length of object = `1/(1/20) × 12` 

= 20 × 12

= 240 cm 

= `240/100​ `

= 2.4 m.

By formula,

⇒ Breadth of model = k × Breadth of object

⇒ Breadth of object = `1/k`​ × Breadth of model

⇒ Breadth of object = `1/(1/20) × 7`

= 20 × 7

= 140 cm

= `140/100​` 

= 1.4 m.