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Concept explainers
15. Geometry A semicircle of radius r is inscribed in a rectangle so that the diameter of the semicircle is the length of the rectangle. See the figure
(a) Express the area A of the rectangle as a function of the radius r of the semicircle.
(b) Express the perimeter p of the rectangle as a function of r.
![Check Mark](/static/check-mark.png)
To find:
a. To express the Area of the rectangle as a function of radius of the semicircle.
Answer to Problem 15AYU
Solution:
a.
Explanation of Solution
Given:
A semicircle of radius is inscribed in a rectangle, so that the diameter of the semicircle is the length of the rectangle as given below.
Calculation:
a. To express the Area of the rectangle as a function of radius of the semicircle:
Area A of the rectangle .
Since the semicircle is inscribed inside the rectangle.
Hence area .
![Check Mark](/static/check-mark.png)
To find:
b. To express the Perimeter of the rectangle as a function of .
Answer to Problem 15AYU
Solution:
b.
Explanation of Solution
Given:
A semicircle of radius is inscribed in a rectangle, so that the diameter of the semicircle is the length of the rectangle as given below.
Calculation:
b. To express the Perimeter of the rectange as a function of .
Perimeter of the rectangle
Therefore, .
Chapter 2 Solutions
Precalculus Enhanced with Graphing Utilities
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