Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
Related questions
Question
![### Review Question
**Problem Statement:**
Rectangles L and M are similar. If the area of rectangle L is 12, what is the area of rectangle M?
**Details Provided:**
1. **Rectangle L:**
- Area = 12
2. **Rectangle M:**
- No specific dimensions or area provided directly.
**Visual Aids:**
- A diagram is provided that shows the relationship between Rectangle L and Rectangle M, indicating that Rectangle M has a scaling factor (1.4) relative to Rectangle L.
**Explanation:**
Since the rectangles are similar, their areas are proportional to the square of the corresponding linear dimensions. If one linear dimension ratio is given as 1.4, this ratio is squared to find the ratio of the areas.
**Calculations:**
1. Linear dimension ratio = 1.4
2. Area ratio = (1.4)^2 = 1.96
Therefore, if the area of rectangle L is 12, the area of rectangle M can be calculated as:
\[ \text{Area of Rectangle M} = 12 \times 1.96 = 23.52 \]
**Conclusion:**
The area of rectangle M is 23.52 square units.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffceb4de4-226d-4fc7-ac8f-83def6c327b8%2Fb567e611-58a9-498e-a340-0341308e8d1a%2Fv9fgrgj_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Review Question
**Problem Statement:**
Rectangles L and M are similar. If the area of rectangle L is 12, what is the area of rectangle M?
**Details Provided:**
1. **Rectangle L:**
- Area = 12
2. **Rectangle M:**
- No specific dimensions or area provided directly.
**Visual Aids:**
- A diagram is provided that shows the relationship between Rectangle L and Rectangle M, indicating that Rectangle M has a scaling factor (1.4) relative to Rectangle L.
**Explanation:**
Since the rectangles are similar, their areas are proportional to the square of the corresponding linear dimensions. If one linear dimension ratio is given as 1.4, this ratio is squared to find the ratio of the areas.
**Calculations:**
1. Linear dimension ratio = 1.4
2. Area ratio = (1.4)^2 = 1.96
Therefore, if the area of rectangle L is 12, the area of rectangle M can be calculated as:
\[ \text{Area of Rectangle M} = 12 \times 1.96 = 23.52 \]
**Conclusion:**
The area of rectangle M is 23.52 square units.
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