A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window (see the figure below). If the perimeter of the window is 11 meters (shown in magenta in the figure), determine the horizontal width of the window (shown in cyan) that will let the most sunlight in.
A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window (see the figure below). If the perimeter of the window is 11 meters (shown in magenta in the figure), determine the horizontal width of the window (shown in cyan) that will let the most sunlight in.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window (see the figure below). If the perimeter of the window is 11 meters (shown in magenta in the figure), determine the horizontal width of the window (shown in cyan) that will let the most sunlight in.
Transcribed Image Text:The image shows a geometric shape combining a semicircle on top of a rectangle. The overall shape resembles a house or a tombstone.
Key Features:
1. **Outline**: The complete shape is outlined with a bold magenta line. The semicircle seamlessly transitions into the rectangle, forming a continuous perimeter.
2. **Dashed Line**: A horizontal blue dashed line runs across the width of the shape, situated at the top of the rectangle, aligned where the semicircle connects with the rectangle.
### Diagram Explanation
- **Semicircle**: The top half of the shape is a perfect semicircle. The straight part of the semicircle sits on the rectangle, and its curved boundary forms the uppermost part of the entire shape.
- **Rectangle**: The lower section is a rectangle, providing a flat base. Its width matches the diameter of the semicircle, ensuring the outline is smooth and proportional.
- **Dashed Line**: The blue dashed line signifies a separation or significant division between the semicircle and the rectangle, potentially indicating a point of measurement or reference line.
This shape is often used in mathematical contexts to discuss composite figures, perimeter, and area calculations.
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