BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015

15th Edition

ISBN: 9781608408405

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Cengage Learning

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Question

Chapter 3.4, Problem 69E

To determine

To calculate: The width of the deck should be when the total area of the pool and deck is 400 feet. Also, find the width of the deck.

Expert Solution & Answer

Answer to Problem 69E

The required width of the rectangular pool is 3.5 feet.

Explanation of Solution

Given information:

The measure of rectangular pool =18 feet by 9 feet

The length of the pool is 18 feet and width of the pool is 9 feet.

It is known that the area of the pool is A=length×width .

Write the translation of the above equation as:

(18+2x)(8+2x)=4004x2+36x+18x+162=4004x2+54x+162−400=04x2+54x−238=0

Simplify the above equation as:

4x22+54x2−2382=022x2+27x−119=0

Solve the above equation by factorization method.

2x2+27x−119=02x2+34x−7x−119=02x(x+17)−7(x+17)=0(x+17)(2x−7)=0

Solve for x .

x+17=0x=−17

And, 2x−7=02x2=72x=72x=3.5

But measurement cannot be negative.

Hence, the required width of the rectangular pool is 3.5 feet.

Chapter 3.4, Problem 68E

Chapter 3.4, Problem 70E

Chapter 3 Solutions

BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015

Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E

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