Algebra: Structure And Method, Book 1

(REV)00 Edition

ISBN: 9780395977224

Author: Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole

Publisher: McDougal Littell

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Concept explainers

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.

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Question

Chapter 1.7, Problem 16P

To determine

To calculate: Solve using the five-stepplan.A rectangle and a square have the same width, but the rectangle is 5 m longer than the square. Their total area is 133 m2 . Find the dimensions of each figure. Choices for the square's width: 6, 7, 8.

Expert Solution & Answer

Answer to Problem 16P

The width of rectangleand square is a=7 m and the length of rectangle is a+5=7+5=12 m

Explanation of Solution

Given information:A rectangle and a square have the same width but the rectangle is 5 m longer than the square and their total area is 133 m2 .

Calculation:

Step 1: Here we have two unknowns, length of the rectangle and width of square and rectangle.

Step 2: Let a be the width of square and rectangle and a+7 be the length of rectangle.

Step 3: As given, their total area is 133 m2 , such that a2+a(a+5)=133

Step 4: Choices for a are given as 6, 7, 8.

a	a2+a(a+5)=133	True / False
6	62+6(6+5)=133	False
7	72+7(7+5)=133	True
8	82+8(8+5)=133	False

From above table we can say that the width of rectangle and square is a=7 m and the length of rectangle is a+5=7+5=12 m

Step 5: Now we verify the answer

The length is 5 m longer than the length of square, such that 12−7=5 which is correct

The total area is 133 m2 : 72+7(12)=133 , which is also correct.

Chapter 1.7, Problem 15P

Chapter 1.7, Problem 17P

Chapter 1 Solutions

Algebra: Structure And Method, Book 1

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