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8. The area of a rectangle whose perimeter is a fixed 80 feet is given by A= 40w– w² , where w is the width of the rectangle. Determine the width of the rectangle that gives the maximum area. What type of special rectangle is necessary to produce this maximum area? Justify.

8. The area of a rectangle whose perimeter is a fixed 80 feet is given by A= 40w– w² , where w is the width of the rectangle. Determine the width of the rectangle that gives the maximum area. What type of special rectangle is necessary to produce this maximum area? Justify.

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.
Chapter8: Areas Of Polygons And Circles
Section8.CR: Review Exercises
Problem 38CR: Prove that if semicircles are constructed on each of the sides of a right triangle, then the area of...
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8. The area of a rectangle whose perimeter is a fixed 80 feet is given by A= 40w-w² , where w is the width of the rectangle. Determine the width of the rectangle that gives the maximum area. What type of special rectangle is necessary to produce this maximum area? Justify.
Transcribed Image Text:8. The area of a rectangle whose perimeter is a fixed 80 feet is given by A= 40w-w² , where w is the width of the rectangle. Determine the width of the rectangle that gives the maximum area. What type of special rectangle is necessary to produce this maximum area? Justify.
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