Geometry: Common Core (15th Edition)

Published by Prentice Hall
ISBN 10: 0133281159
ISBN 13: 978-0-13328-115-6

Chapter 7 - Similarity - Mid-Chapter Quiz - Page 459: 6


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.
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