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Consider the reduction of the rectangle.

A larger rectangle has a length of 18 inches and width of 8 inches. A smaller rectangle has a length of x inches and width of 3 inches.

Write a proportion and then solve to find the missing measure of the reduced rectangle.

What two ratios can be used in the proportion?

8/3 and 18/x

1 answer

To set up a proportion based on the ratios of the dimensions of the larger and smaller rectangles, you can compare the lengths and widths:

  1. The ratio of the width of the larger rectangle to the width of the smaller rectangle is: \[ \frac{8}{3} \]

  2. The ratio of the length of the larger rectangle to the length of the smaller rectangle is: \[ \frac{18}{x} \]

Now, since these two ratios should be equal to each other, you can write the proportion as: \[ \frac{8}{3} = \frac{18}{x} \]

To solve for \( x \), you can cross-multiply: \[ 8x = 3 \times 18 \] \[ 8x = 54 \]

Now, divide both sides by 8: \[ x = \frac{54}{8} = 6.75 \]

Thus, the missing measure of the smaller rectangle is \( x = 6.75 \) inches.

Summary:

The two ratios that can be used in the proportion are: \[ \frac{8}{3} \text{ and } \frac{18}{x} \] And the value of \( x \) is \( 6.75 \) inches.