Algebra and Trigonometry: Structure and Method, Book 2

2000th Edition

ISBN: 9780395977255

Author: MCDOUGAL LITTEL

Publisher: McDougal Littell

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Question

Chapter 7, Problem 14CT

To determine

Tofind: thedimensions of the rectangle of greatest area whose perimeter is 20 cm.

Expert Solution & Answer

Answer to Problem 14CT

The dimensions of the rectangle of greatest areaare 5cm and 5cm whose perimeter is 20 cm.

Explanation of Solution

Given information:

Perimeter of rectangle is 20 cm.

Calculation: to find the dimensions, let x is the length of the rectangle and y is the width of the rectangle.

2(x+y)=20x+y=10 [divide]y=10−x [subtract]

Thus, the area of the rectangle can be defined as:

a=x(10−x)a=10x−x2 [multiply]

To find the greatest area, first differentiate and then put equal to zero,

a=10x−x2a'=10−2x [differentiate]10−2x=0 [equal to zero]x=5 [simplify]

Thus, the dimensions of the rectangle is 5cm and 5cm .

Chapter 7, Problem 13CT

Chapter 7, Problem 1CLR

Chapter 7 Solutions

Algebra and Trigonometry: Structure and Method, Book 2

Ch. 7.1 - Prob. 1OE Ch. 7.1 - Prob. 2OE Ch. 7.1 - Prob. 3OE Ch. 7.1 - Prob. 4OE Ch. 7.1 - Prob. 5OE Ch. 7.1 - Prob. 6OE Ch. 7.1 - Prob. 7OE Ch. 7.1 - Prob. 8OE Ch. 7.1 - Prob. 9OE Ch. 7.1 - Prob. 10OE

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