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A rectangular garden is fenced on three sides, and the house forms the fourth side of the rectangle. a. Given that the total length of the fence is 80 m, present an illustration of the problem. b. Show that the area, A, is given by the formula A=y(80-2y), where y is the distance from the house to the end of the garden. c. Given that the area is a maximum for the length of this garden, find the dimensions of the enclosed garden and the area which is enclosed.

A rectangular garden is fenced on three sides, and the house forms the fourth side of the rectangle. a. Given that the total length of the fence is 80 m, present an illustration of the problem. b. Show that the area, A, is given by the formula A=y(80-2y), where y is the distance from the house to the end of the garden. c. Given that the area is a maximum for the length of this garden, find the dimensions of the enclosed garden and the area which is enclosed.

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter9: Polynomial And Rational Functions
Section9.4: Graphing Polynomial Functions
Problem 43PS
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A rectangular garden is fenced on three sides, and the house forms the fourth side of the rectangle. a. Given that the total length of the fence is 80 m, present an illustration of the problem. b. Show that the area, A, is given by the formula A=y(80-2y), where y is the distance from the house to the end of the garden. c. Given that the area is a maximum for the length of this garden, find the dimensions of the enclosed garden and the area which is enclosed.
Transcribed Image Text:A rectangular garden is fenced on three sides, and the house forms the fourth side of the rectangle. a. Given that the total length of the fence is 80 m, present an illustration of the problem. b. Show that the area, A, is given by the formula A=y(80-2y), where y is the distance from the house to the end of the garden. c. Given that the area is a maximum for the length of this garden, find the dimensions of the enclosed garden and the area which is enclosed.
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