The dimensions of the model of a multistorey building are 1.2 m × 75 cm × 2 m. If the scale factor is 1 : 30; find the actual dimensions of the building.

Dimensions of model = 1.2 m × 75 cm × 2 m = 1.2 m × 0.75 m × 2 m

So,

Length = 1.2 m

Breadth = 0.75 m

Height = 2 m.

$\phantom{\Rightarrow} \dfrac{\text{Length of model}}{\text{Length of building}} = k \\[1em] \Rightarrow \dfrac{1.2}{\text{Length of building}} = \dfrac{1}{30} \\[1em] \Rightarrow \text{Length of building} = 1.2 \times 30 = 36 \text{ m}. \\[2em] \phantom{\Rightarrow} \dfrac{\text{Breadth of model}}{\text{Breadth of building}} = k \\[1em] \Rightarrow \dfrac{0.75}{\text{Breadth of building}} = \dfrac{1}{30} \\[1em] \Rightarrow \text{Breadth of building} = 0.75 \times 30 = 22.5 \text{ m}. \\[2em] \phantom{\Rightarrow} \dfrac{\text{Height of model}}{\text{Height of building}} = k \\[1em] \Rightarrow \dfrac{\text{2}}{\text{Height of building}} = \dfrac{1}{30} \\[1em] \Rightarrow \text{Height of building} = 2 \times 30 = 60 \text{ m}.$

Hence, actual dimension of building = 36 m × 22.5 m × 60 m.