#### Answer

The room is $17.5$ feet long.

#### Work Step by Step

In the scale drawing, $2$ in. = $5$ ft.
The lengths are in different units, so let's convert them to the same unit.
Let's convert feet to inches. There are $12$ inches in one foot. We can express the conversion factor as a proportion:
$\frac{1}{12} = \frac{5}{x}$
Use the cross products property to get rid of the fractions:
$x = 60$
There are $60$ inches in $5$ feet.
Let's put together the proportion:
$\frac{2}{60} = \frac{7}{x}$
Use the cross product property:
$2x = 420$
Divide both sides by $x$:
$x = 210$
This measurement is in inches. Let's convert it into feet using the conversion factor:
$\frac{1}{12} = \frac{x}{210}$
Use the cross products property to eliminate the fractions:
$12x = 210$
Divide both sides by $12$ to solve for $x$:
$x = \frac{210}{12}$
Simplify the fraction by dividing both the numerator and denominator by their greatest common factor, $6$:
$x = \frac{35}{2}$
Divide to solve:
$x = 17.5$
The room is $17.5$ feet long.