two rectangles are similar the first one 8 feet wide and 32 feet long the second is 12 feet wide. what is the length of the second rectangle

The two rectangles are similar, which means that their corresponding sides are proportional. 

Let the width of the first rectangle be \( 8 \) feet, the length of the first rectangle be \( 32 \) feet, the width of the second rectangle be \( 12 \) feet, and the unknown length of the second rectangle be \( L \).

Since the rectangles are similar, the ratio of the widths is equal to the ratio of the lengths:

\[
\frac{8}{32} = \frac{12}{L}
\]

Simplify the left side:

\[
\frac{1}{4} = \frac{12}{L}
\]

Now solve for \( L \):

\[
L = 12 \times 4 = 48
\]

Thus, the length of the second rectangle is **48 feet**.

Would you like any further explanation or details?

Here are some related questions for further practice:
1. If the width of the second rectangle was 10 feet, what would the length be?
2. What is the area of each rectangle?
3. What is the perimeter of each rectangle?
4. If the first rectangle were scaled by a factor of 2, what would its new dimensions be?
5. How do you calculate the diagonal of a rectangle?

**Tip:** When dealing with similar shapes, always remember to set up a proportion based on corresponding sides.

Two rectangles are similar. The first one is 8 feet wide and 32 feet long. The second is 12 feet wide. What is the length of the second rectangle?

Learn how to find the length of a similar rectangle given that the first rectangle is 8 feet wide and 32 feet long, and the second rectangle is 12 feet wide. This problem covers proportions and similarity of shapes, suitable for students in Grades 6-8.

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