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# help

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A company makes rugs. Their smallest rug is a 2 ft by 3 ft rectangle. The largest rug is a similair rectangle. If one side of their largestrug is 18 ft, what are the possible dimensions of their rug

Jan 14, 2020

#2
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18,27 and 12,18

Jan 14, 2020
#3
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Since we know that their largest rug is a similar rectangle, i.e. having the same proportional shape to their smallest rug, there are two possibilities for the dimensions of the largest rug: either the largest rug's 18ft side is similar to the 2ft side or the 3ft side. This gives us an 18ft by $$x$$ ft rectangle and a $$y$$ ft by 18 ft rectangle. Using the original proportions, we can now solve for $$x$$ and $$y$$:

$$\frac{3}{2}=\frac{x}{18} \rightarrow x = 18* \frac{3}{2} \rightarrow x = 27$$

$$\frac{2}{3} = \frac{y}{18} \rightarrow y = 18 * \frac{2}{3} \rightarrow y = 12$$

Thus, the company's largest rug dimensions are either 18 ft by 27 ft or 12 ft by 18 ft. Hope this helps!

Jan 14, 2020
#4
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Proportions:      2 : 3 = 18 : X     X = 3 * 18 / 2      X = 27

3 : 2 = 18 : Y     Y = 2 * 18 / 3      Y = 12 Jan 14, 2020