Question

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?


What is the value of the missing measure?

Answer 1

To set up the proportion for the reduction of the rectangle, we can compare the corresponding dimensions of the larger and smaller rectangles.

The larger rectangle has dimensions:
- Length = 18 inches
- Width = 8 inches

The smaller rectangle has dimensions:
- Length = x inches
- Width = 3 inches

The two ratios that can be used in the proportion can be written as:

\[
\frac{\text{Length of larger rectangle}}{\text{Length of smaller rectangle}} = \frac{\text{Width of larger rectangle}}{\text{Width of smaller rectangle}}
\]

This gives us the proportion:

\[
\frac{18}{x} = \frac{8}{3}
\]

Next, we can solve for \(x\) by cross-multiplying:

\[
18 \cdot 3 = 8 \cdot x
\]

Calculating \(18 \cdot 3\):

\[
54 = 8x
\]

Now, divide both sides by 8 to isolate \(x\):

\[
x = \frac{54}{8} = 6.75
\]

Therefore, the value of the missing measure (length of the smaller rectangle) is \(\boxed{6.75}\) inches.