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
+150 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!
