To find the original rectangle before it was enlarged by a scale factor of 1.5, we need to divide the dimensions of the enlarged rectangle by 1.5.
Let’s denote the dimensions of the original rectangle as \( L \) (length) and \( W \) (width). The relationship with the enlarged rectangle can be expressed as:
- Enlarged Length = \( L \times 1.5 \)
- Enlarged Width = \( W \times 1.5 \)
From the information provided:
- The larger rectangle has a length of 18 and a width of 4.
Now we can find the original dimensions of the rectangle:
- Original Length: \[ L = \frac{18}{1.5} = 12 \]
- Original Width: \[ W = \frac{4}{1.5} = \frac{4}{1.5} = \frac{8}{3} \approx 2.67 \]
However, none of the rectangular dimensions given perfectly match the width of \( \approx 2.67 \).
Now let’s look at the options given to find the original rectangle:
- Length 12 and Width 3.
- Length 18 and Width 4.
- Length 8 and Width 2.
- Length 8 and Width 3.
Introducing the values again:
- The length of the original rectangle (before enlargement) is determined to be 12.
- The original width (after dividing \( 4 \) by \( 1.5 \)) comes out to be approximately 2.67, but none of the given rectangles with widths align closely.
The only rectangle that has the correct length (12) is option 1:
- Length: 12 and Width: 3
Even though the width doesn't align exactly, it matches the calculated length, suggesting that the original rectangle could be placed at the edge of the scale.
Therefore, the best option, based on the scale enlargement of \( 12 \times 3 \) and the given dimensions, is:
Option 1: On a coordinate plane, a rectangle has a length of 12 and width of 3.
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