Question
Shawna reduced the size of a rectangle to a height of 2 in. What is the new width if it was originally 24 in wide and 12 in tall?
Ask by Bob Marsh. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The new width is 4 inches.
Solution
To determine the new width of the rectangle after reducing its size, we'll assume that the rectangle is scaled proportionally. This means that both the width and height are reduced by the same scale factor to maintain the rectangle's original shape.
**Original Dimensions:**
- **Width:** 24 inches
- **Height:** 12 inches
**New Height:** 2 inches
**Step 1: Calculate the Scale Factor**
The scale factor is determined by the ratio of the new height to the original height.
\[
\text{Scale Factor} = \frac{\text{New Height}}{\text{Original Height}} = \frac{2\, \text{in}}{12\, \text{in}} = \frac{1}{6}
\]
**Step 2: Apply the Scale Factor to the Width**
\[
\text{New Width} = \text{Original Width} \times \text{Scale Factor} = 24\, \text{in} \times \frac{1}{6} = 4\, \text{in}
\]
**Conclusion:**
After reducing the size proportionally, the new width of the rectangle is **4 inches**.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution The Deep Dive
When Shawna reduced the height of the rectangle to 2 inches, she maintained the same aspect ratio. The original ratio of width to height is 24:12, which simplifies to 2:1. Since the new height is 2 inches, the new width must be double that, which is 4 inches. So, the rectangle now measures 4 inches wide and 2 inches tall! This exercise in scaling rectangles can come in handy in real-life scenarios, such as designing posters or other visual media. Understanding proportions is key, as it helps you maintain the intended appearance when resizing and ensures that your designs are visually appealing and proportionate.
