Question

John has a blueprint of a building which is designed with a scale factor $1:12$. The dimensions of a room in the blueprint is $10\text{in.}\times 8\text{in.}\times 12\text{in.}$
Find the actual dimension of the room.

• A. $10\text{ft.}\times 8\text{ft.}\times 12\text{ft.}$
• B. $120\text{ft.}\times 96\text{ft.}\times 144\text{ft.}$
• C. $100\text{ft.}\times 80\text{ft.}\times 120\text{ft.}$
• D. None of the above

Answer 1

The correct option is A $10\text{ft.}\times 8\text{ft.}\times 12\text{ft.}$

$\text{Given:}$
$\bullet$ Dimensions in the blueprint is
$10\text{in.}\times 8\text{in.}\times 12\text{in.}$
$\bullet$ Scale factor = $\frac{1}{12}$

We know that,
$\text{Scale factor}=\frac{\text{Dimension of scale model}}{\text{Dimension of actual object}}$

$\Rightarrow \text{Dimension of actual object}=\frac{\text{Dimension of scale model}}{\text{Scale factor}}$

= $\frac{\text{Dimension of scale model}}{\frac{1}{12}}$

= $\text{Dimension of scale model}\times 12$

Hence, the actual dimensions can be found by multiplying the corresponding dimensions in the blueprint by $12$.

$\to (10\text{in.}\times 12)\times (8\text{in.}\times 12)\times (12\text{in.}\times 12$
$=120\text{in.}\times 96\text{in.}\times 144\text{in.}$

But, we need the dimensions in feet.
We know, $12\text{inches}=1\text{foot}$

Hence, the actual dimensions in feet are,

$\frac{120}{12}\text{ft.}\times \frac{96}{12}\text{ft.}\times \frac{144}{12}\text{ft.}$
$=10\text{ft.}\times 8\text{ft.}\times 12\text{ft.}$