# A garage floor measures 150 feet by 120 feet. A scale drawing of the floor on grid paper uses a scale of 1 unit 15 feet. What are the dimensions of the drawing?

Apr 30, 2017

10 feet by 8 feet

#### Explanation:

I choose the following:

Actual width $\to {W}_{a} = 150 f t$
Scaled width $\to {W}_{s}$

Actual length $\to {L}_{a} = 120 f t$
Scaled length $\to {L}_{s}$

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Consider width - first principles}}$

Using ratio in fraction format gives:

$\left(\text{Actual")/("Scaled}\right) \to \frac{15}{1} \equiv {W}_{a} / {W}_{s} = \frac{150}{W} _ s$

Turn up the other way (should have done that at the beginning!)

$\left(\text{Scaled")/("Actual}\right) \to \frac{1}{15} \equiv {W}_{s} / 150$

color(green)(1/15color(red)(xx1)-=W_s/150

color(green)(1/15color(red)(xx10/10)=W_s/150

$\frac{10}{150} = {W}_{s} / 150$

${W}_{s} \to \text{ scale width } = 10 f e e t$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Consider length}}$

$\textcolor{b r o w n}{\text{Using short cut method}}$

${L}_{s} / {L}_{a} \to \frac{1}{15} \equiv {L}_{s} / 120$

Multiply both sides by 120

${L}_{s} = 8 f e e t$