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Scale facto(- Arca lectangles E and Fare similak. TE the are of rectangie E IS ab. what Is the area of rectargle F! 16 12.8 aatang (CE Arca9b Rcctara k

Scale facto(- Arca lectangles E and Fare similak. TE the are of rectangie E IS ab. what Is the area of rectargle F! 16 12.8 aatang (CE Arca9b Rcctara k

Elementary Geometry For College Students, 7e
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
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**Scale Factor - Area** **Problem Statement:** Rectangles E and F are similar. If the area of Rectangle E is 96, what is the area of Rectangle F? **Detailed Explanation:** We are given two rectangles, Rectangle E and Rectangle F, which are similar. The area of Rectangle E is 96 square units. The goal is to determine the area of Rectangle F. **Diagram Description:** There are two rectangles drawn on graph paper. - The first rectangle is labeled "Rectangle E" and has an area of 96. - The second rectangle is labeled "Rectangle F" and is associated with another value, 12.8. Between these two diagrams, the scale factor 16 is written. **Solution Approach:** Given that the rectangles are similar, the ratio of their areas would be the square of the scale factor. Suppose the scale factor from Rectangle E to Rectangle F is `k`, then: (Area of Rectangle F) / (Area of Rectangle E) = `k^2` Using the given data: - Area of Rectangle E = 96 - Rectangle F has 16 written next to it To find Area of Rectangle F: 1. Identify and use the given scale factor. 2. Multiply the area of Rectangle E by the scale factor squared. However, based on the information provided, it's not straightforward since the values seem to represent scale factor and an unknown area. More context would be required to finalize the mathematical solution correctly, or a clearer value (such as the written 12.8) suggests that additional steps might be required to ensure correctness.
Transcribed Image Text:**Scale Factor - Area** **Problem Statement:** Rectangles E and F are similar. If the area of Rectangle E is 96, what is the area of Rectangle F? **Detailed Explanation:** We are given two rectangles, Rectangle E and Rectangle F, which are similar. The area of Rectangle E is 96 square units. The goal is to determine the area of Rectangle F. **Diagram Description:** There are two rectangles drawn on graph paper. - The first rectangle is labeled "Rectangle E" and has an area of 96. - The second rectangle is labeled "Rectangle F" and is associated with another value, 12.8. Between these two diagrams, the scale factor 16 is written. **Solution Approach:** Given that the rectangles are similar, the ratio of their areas would be the square of the scale factor. Suppose the scale factor from Rectangle E to Rectangle F is `k`, then: (Area of Rectangle F) / (Area of Rectangle E) = `k^2` Using the given data: - Area of Rectangle E = 96 - Rectangle F has 16 written next to it To find Area of Rectangle F: 1. Identify and use the given scale factor. 2. Multiply the area of Rectangle E by the scale factor squared. However, based on the information provided, it's not straightforward since the values seem to represent scale factor and an unknown area. More context would be required to finalize the mathematical solution correctly, or a clearer value (such as the written 12.8) suggests that additional steps might be required to ensure correctness.
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