Question

A small aeroplane has a wing span of $15\text{feet}.$ The scale factor for a model of the aeroplane is $\frac{1}{60}$. Find the wing span of the model in inches.

• A. $2$
• B. $3$
• C. $4$
• D. $6$

Answer 1

The correct option is B $3$

$\text{Given:}$
$\bullet$ Actual wing span = $15\text{feet}$
$\bullet$ Scale factor = $\frac{1}{60}$

Let, wing span of the model = $x\text{feet}$

We know that,

$\text{Scale factor}$

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

$\Rightarrow \frac{1}{60}=\frac{x}{15}$

Multiplying both sides by $60$,
$\Rightarrow \frac{1}{60}\times 60=\frac{x}{15}\times 60$
$\Rightarrow 1=x\times 4$

Dividing both sides by $4$,
$\Rightarrow \frac{1}{4}=\frac{x\times 4}{4}$
$\Rightarrow \frac{1}{4}=x$

$\therefore$ Wing span of the model = $\frac{1}{4}\text{foot}$

But we need to find the wing span of the model in inches.

$\because$ $1\text{foot}=12\text{inches}$
$\therefore$ $\frac{1}{4}\text{foot}=\frac{1}{4}\times 12\text{inches}=3\text{inches}$

Hence, option (b.) is correct.