Question

consider the reduction of the rectangle.
write a proportion and then solve to find the missing measure of the reduced rectangle.
what two ratios can be used in the proportion?
what is the value of the missing measure?

Explanation:

Step1: Set up the proportion

Since the rectangles are similar, the ratios of corresponding sides are equal. The ratios can be \(\frac{3}{6}\) (ratio of the shorter sides of the two rectangles) and \(\frac{x}{18}\) (ratio of the longer sides of the two rectangles). So the proportion is \(\frac{3}{6}=\frac{x}{18}\).

Step2: Cross - multiply to solve for \(x\)

Cross - multiplying gives \(6x = 3\times18\).

Step3: Simplify the right - hand side

\(3\times18 = 54\), so the equation becomes \(6x=54\).

Step4: Solve for \(x\)

Divide both sides of the equation \(6x = 54\) by \(6\). We get \(x=\frac{54}{6}=9\).

Answer:

The two ratios that can be used in the proportion are \(\frac{3}{6}\) and \(\frac{x}{18}\). The value of the missing measure \(x\) is \(9\).