(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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Question

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 3.5, Problem 13P

To determine

To find: the length of the longest side of triangle

Expert Solution & Answer

Answer to Problem 13P

The length of the longest side of the triangle is 14

Explanation of Solution

Given information: “The lengths of the sides of a triangle are consecutive even integers”, “The length of the longest side if it is 22 units shorter than the perimeter”

Concept Involved:

Perimeter of triangle means sum of all the sides of the triangle.

Assign variable for the unknown that we need to find.

Use the keywords in the statement to rewrite the statement to meaningful math equation.

“is” means =

“shorter than” means -

Solve the equation by getting the variable in one side of the equation and undoing whatever is done to it by performing reverse operation.

Calculation: Assign variable for the unknown that we need to find

The three sides of the triangle given that they are consecutive even integer can be represented by

x, x+2, x+4 where x is the smallest side, x+ 2 is middle side & x + 4 is largest side of the triangle.

Rewrite the sentence using the variable representing largest side and perimeter

x+4 is 22 shorter than the perimeter {The sum of all the sides}

Replace the keywords to get an equation representing the sentence given

x+4=(x+x+2+x+4)−22

Combine like terms in right side of the equation

x+4=3x−16

In the process of getting x in one side of the equation subtract 3x on both sides

x+4−3x=3x−16−3x

Combine like terms on both sides

−2x+4=−16

Subtract 4 on both sides of the equation

−2x+4−4=−16−4

Combine like terms on both sides of the equation

−2x=−20

Divide -2 on both sides of the equation

−2x−2=−20−2

Simplify fraction on both sides of the equation

x=10

Substitute 10 for x in the expression x+4 to find the larger side

10+4=14

Conclusion:

The smallest side is 10, middle side is 12 and largest side of the triangle is 14

Chapter 3.5, Problem 12P

Chapter 3.5, Problem 14P

Chapter 3 Solutions

Algebra: Structure And Method, Book 1

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

Ch. 3.1 - Prob. 11OE Ch. 3.1 - Prob. 12OE Ch. 3.1 - Prob. 13OE Ch. 3.1 - Prob. 14OE Ch. 3.1 - Prob. 15OE Ch. 3.1 - Prob. 16OE Ch. 3.1 - Prob. 17OE Ch. 3.1 - Prob. 18OE Ch. 3.1 - Prob. 19OE Ch. 3.1 - Prob. 20OE Ch. 3.1 - Prob. 21OE Ch. 3.1 - Prob. 1WE Ch. 3.1 - Prob. 2WE Ch. 3.1 - Prob. 3WE Ch. 3.1 - Prob. 4WE Ch. 3.1 - Prob. 5WE Ch. 3.1 - Prob. 6WE Ch. 3.1 - Prob. 7WE Ch. 3.1 - Prob. 8WE Ch. 3.1 - Prob. 9WE Ch. 3.1 - Prob. 10WE Ch. 3.1 - Prob. 11WE Ch. 3.1 - Prob. 12WE Ch. 3.1 - Prob. 13WE Ch. 3.1 - Prob. 14WE Ch. 3.1 - Prob. 15WE Ch. 3.1 - Prob. 16WE Ch. 3.1 - Prob. 17WE Ch. 3.1 - Prob. 18WE Ch. 3.1 - Prob. 19WE Ch. 3.1 - Prob. 20WE Ch. 3.1 - Prob. 21WE Ch. 3.1 - Prob. 22WE Ch. 3.1 - Prob. 23WE Ch. 3.1 - Prob. 24WE Ch. 3.1 - Prob. 25WE Ch. 3.1 - Prob. 26WE Ch. 3.1 - Prob. 27WE Ch. 3.1 - Prob. 28WE Ch. 3.1 - Prob. 29WE Ch. 3.1 - Prob. 30WE Ch. 3.1 - Prob. 31WE Ch. 3.1 - Prob. 32WE Ch. 3.1 - Prob. 33WE Ch. 3.1 - Prob. 34WE Ch. 3.1 - Prob. 35WE Ch. 3.1 - Prob. 36WE Ch. 3.1 - Prob. 37WE Ch. 3.1 - Prob. 38WE Ch. 3.1 - Prob. 39WE Ch. 3.1 - Prob. 40WE Ch. 3.1 - Prob. 41WE Ch. 3.1 - Prob. 42WE Ch. 3.1 - Prob. 43WE Ch. 3.1 - Prob. 44WE Ch. 3.1 - Prob. 45WE Ch. 3.1 - Prob. 46WE Ch. 3.1 - Prob. 47WE Ch. 3.1 - Prob. 48WE Ch. 3.1 - Prob. 49WE Ch. 3.1 - Prob. 50WE Ch. 3.1 - Prob. 51WE Ch. 3.1 - Prob. 52WE Ch. 3.1 - Prob. 53WE Ch. 3.1 - Prob. 54WE Ch. 3.1 - Prob. 55WE Ch. 3.1 - Prob. 56WE Ch. 3.1 - Prob. 57WE Ch. 3.1 - Prob. 58WE Ch. 3.1 - Prob. 59WE Ch. 3.1 - Prob. 60WE Ch. 3.1 - Prob. 1P Ch. 3.1 - Prob. 2P Ch. 3.1 - Prob. 3P Ch. 3.1 - Prob. 4P Ch. 3.1 - Prob. 5P Ch. 3.1 - Prob. 6P Ch. 3.1 - Prob. 7P Ch. 3.1 - Prob. 8P Ch. 3.1 - Prob. 9P Ch. 3.1 - Prob. 10P Ch. 3.1 - Prob. 11P Ch. 3.1 - Prob. 12P Ch. 3.1 - Prob. 13P Ch. 3.1 - Prob. 14P Ch. 3.1 - Prob. 15P Ch. 3.1 - Prob. 16P Ch. 3.1 - Prob. 17P Ch. 3.1 - Prob. 18P Ch. 3.1 - Prob. 19P Ch. 3.1 - Prob. 20P Ch. 3.1 - Prob. 1MRE Ch. 3.1 - Prob. 2MRE Ch. 3.1 - Prob. 3MRE Ch. 3.1 - Prob. 4MRE Ch. 3.1 - Prob. 5MRE Ch. 3.1 - Prob. 6MRE Ch. 3.1 - Prob. 7MRE Ch. 3.1 - Prob. 8MRE Ch. 3.1 - Prob. 9MRE Ch. 3.1 - Prob. 10MRE Ch. 3.1 - Prob. 11MRE Ch. 3.1 - Prob. 12MRE Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.2 - Prob. 1OE Ch. 3.2 - Prob. 2OE Ch. 3.2 - Prob. 3OE Ch. 3.2 - Prob. 4OE Ch. 3.2 - Prob. 5OE Ch. 3.2 - Prob. 6OE Ch. 3.2 - Prob. 7OE Ch. 3.2 - Prob. 8OE Ch. 3.2 - Prob. 9OE Ch. 3.2 - Prob. 10OE Ch. 3.2 - Prob. 11OE Ch. 3.2 - Prob. 12OE Ch. 3.2 - Prob. 13OE Ch. 3.2 - Prob. 14OE Ch. 3.2 - Prob. 15OE Ch. 3.2 - Prob. 16OE Ch. 3.2 - Prob. 17OE Ch. 3.2 - Prob. 18OE Ch. 3.2 - Prob. 1WE Ch. 3.2 - Prob. 2WE Ch. 3.2 - Prob. 3WE Ch. 3.2 - Prob. 4WE Ch. 3.2 - Prob. 5WE Ch. 3.2 - Prob. 6WE Ch. 3.2 - Prob. 7WE Ch. 3.2 - Prob. 8WE Ch. 3.2 - Prob. 9WE Ch. 3.2 - Prob. 10WE Ch. 3.2 - Prob. 11WE Ch. 3.2 - Prob. 12WE Ch. 3.2 - Prob. 13WE Ch. 3.2 - Prob. 14WE Ch. 3.2 - Prob. 15WE Ch. 3.2 - Prob. 16WE Ch. 3.2 - Prob. 17WE Ch. 3.2 - Prob. 18WE Ch. 3.2 - Prob. 19WE Ch. 3.2 - Prob. 20WE Ch. 3.2 - Prob. 21WE Ch. 3.2 - 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Prob. 19P Ch. 3.2 - Prob. 20P Ch. 3.2 - Prob. 1MRE Ch. 3.2 - Prob. 2MRE Ch. 3.2 - Prob. 3MRE Ch. 3.2 - Prob. 4MRE Ch. 3.2 - Prob. 5MRE Ch. 3.2 - Prob. 6MRE Ch. 3.2 - Prob. 7MRE Ch. 3.2 - Prob. 8MRE Ch. 3.2 - Prob. 9MRE Ch. 3.2 - Prob. 10MRE Ch. 3.2 - Prob. 11MRE Ch. 3.2 - Prob. 12MRE Ch. 3.3 - Prob. 1OE Ch. 3.3 - Prob. 2OE Ch. 3.3 - Prob. 3OE Ch. 3.3 - Prob. 4OE Ch. 3.3 - Prob. 5OE Ch. 3.3 - Prob. 6OE Ch. 3.3 - Prob. 7OE Ch. 3.3 - Prob. 8OE Ch. 3.3 - Prob. 9OE Ch. 3.3 - Prob. 10OE Ch. 3.3 - Prob. 11OE Ch. 3.3 - Prob. 12OE Ch. 3.3 - Prob. 13OE Ch. 3.3 - Prob. 14OE Ch. 3.3 - Prob. 15OE Ch. 3.3 - Prob. 16OE Ch. 3.3 - Prob. 17OE Ch. 3.3 - Prob. 18OE Ch. 3.3 - Prob. 1WE Ch. 3.3 - Prob. 2WE Ch. 3.3 - Prob. 3WE Ch. 3.3 - Prob. 4WE Ch. 3.3 - Prob. 5WE Ch. 3.3 - Prob. 6WE Ch. 3.3 - Prob. 7WE Ch. 3.3 - Prob. 8WE Ch. 3.3 - Prob. 9WE Ch. 3.3 - Prob. 10WE Ch. 3.3 - Prob. 11WE Ch. 3.3 - Prob. 12WE Ch. 3.3 - Prob. 13WE Ch. 3.3 - Prob. 14WE Ch. 3.3 - Prob. 15WE Ch. 3.3 - Prob. 16WE Ch. 3.3 - Prob. 17WE Ch. 3.3 - Prob. 18WE Ch. 3.3 - Prob. 19WE Ch. 3.3 - Prob. 20WE Ch. 3.3 - Prob. 21WE Ch. 3.3 - Prob. 22WE Ch. 3.3 - Prob. 23WE Ch. 3.3 - Prob. 24WE Ch. 3.3 - Prob. 25WE Ch. 3.3 - Prob. 26WE Ch. 3.3 - Prob. 27WE Ch. 3.3 - Prob. 28WE Ch. 3.3 - Prob. 29WE Ch. 3.3 - Prob. 30WE Ch. 3.3 - Prob. 31WE Ch. 3.3 - Prob. 32WE Ch. 3.3 - Prob. 33WE Ch. 3.3 - Prob. 34WE Ch. 3.3 - Prob. 35WE Ch. 3.3 - Prob. 36WE Ch. 3.3 - Prob. 37WE Ch. 3.3 - Prob. 38WE Ch. 3.3 - Prob. 39WE Ch. 3.3 - Prob. 40WE Ch. 3.3 - Prob. 41WE Ch. 3.3 - Prob. 42WE Ch. 3.3 - Prob. 43WE Ch. 3.3 - Prob. 44WE Ch. 3.3 - Prob. 45WE Ch. 3.3 - Prob. 46WE Ch. 3.3 - Prob. 47WE Ch. 3.3 - Prob. 48WE Ch. 3.3 - Prob. 49WE Ch. 3.3 - Prob. 50WE Ch. 3.3 - Prob. 51WE Ch. 3.3 - Prob. 52WE Ch. 3.3 - Prob. 53WE Ch. 3.3 - Prob. 54WE Ch. 3.3 - Prob. 55WE Ch. 3.3 - Prob. 56WE Ch. 3.3 - Prob. 57WE Ch. 3.3 - Prob. 58WE Ch. 3.3 - Prob. 59WE Ch. 3.3 - Prob. 60WE Ch. 3.3 - Prob. 1MRE Ch. 3.3 - Prob. 2MRE Ch. 3.3 - Prob. 3MRE Ch. 3.3 - Prob. 4MRE Ch. 3.3 - Prob. 5MRE Ch. 3.3 - Prob. 6MRE Ch. 3.3 - Prob. 7MRE Ch. 3.3 - Prob. 8MRE Ch. 3.3 - Prob. 9MRE Ch. 3.3 - Prob. 10MRE Ch. 3.3 - Prob. 11MRE Ch. 3.3 - Prob. 12MRE Ch. 3.3 - Prob. 1E Ch. 3.3 - Prob. 2E Ch. 3.3 - Prob. 3E Ch. 3.4 - Prob. 1P Ch. 3.4 - Prob. 2P Ch. 3.4 - Prob. 3P Ch. 3.4 - Prob. 4P Ch. 3.4 - Prob. 5P Ch. 3.4 - Prob. 6P Ch. 3.4 - Prob. 7P Ch. 3.4 - Prob. 8P Ch. 3.4 - Prob. 9P Ch. 3.4 - Prob. 10P Ch. 3.4 - Prob. 11P Ch. 3.4 - Prob. 12P Ch. 3.4 - Prob. 13P Ch. 3.4 - Prob. 14P Ch. 3.4 - Prob. 15P Ch. 3.4 - Prob. 16P Ch. 3.4 - Prob. 17P Ch. 3.4 - Prob. 18P Ch. 3.4 - Prob. 19P Ch. 3.4 - Prob. 20P Ch. 3.4 - Prob. 21P Ch. 3.4 - Prob. 22P Ch. 3.4 - Prob. 23P Ch. 3.4 - Prob. 24P Ch. 3.4 - Prob. 25P Ch. 3.4 - Prob. 26P Ch. 3.4 - Prob. 27P Ch. 3.4 - Prob. 28P Ch. 3.4 - Prob. 29P Ch. 3.4 - Prob. 30P Ch. 3.4 - Prob. 31P Ch. 3.4 - Prob. 32P Ch. 3.4 - Prob. 33P Ch. 3.4 - Prob. 1MRE Ch. 3.4 - Prob. 2MRE Ch. 3.4 - Prob. 3MRE Ch. 3.4 - Prob. 4MRE Ch. 3.4 - Prob. 5MRE Ch. 3.4 - Prob. 6MRE Ch. 3.4 - Prob. 7MRE Ch. 3.4 - Prob. 8MRE Ch. 3.4 - Prob. 9MRE Ch. 3.4 - Prob. 10MRE Ch. 3.4 - Prob. 11MRE Ch. 3.4 - Prob. 12MRE Ch. 3.5 - Prob. 1OE Ch. 3.5 - Prob. 2OE Ch. 3.5 - Prob. 3OE Ch. 3.5 - Prob. 4OE Ch. 3.5 - Prob. 5OE Ch. 3.5 - Prob. 6OE Ch. 3.5 - Prob. 7OE Ch. 3.5 - Prob. 8OE Ch. 3.5 - Prob. 9OE Ch. 3.5 - Prob. 10OE Ch. 3.5 - Prob. 11OE Ch. 3.5 - Prob. 12OE Ch. 3.5 - Prob. 1WE Ch. 3.5 - Prob. 2WE Ch. 3.5 - Prob. 3WE Ch. 3.5 - Prob. 4WE Ch. 3.5 - Prob. 5WE Ch. 3.5 - Prob. 6WE Ch. 3.5 - Prob. 7WE Ch. 3.5 - Prob. 8WE Ch. 3.5 - Prob. 9WE Ch. 3.5 - Prob. 10WE Ch. 3.5 - Prob. 11WE Ch. 3.5 - Prob. 12WE Ch. 3.5 - Prob. 13WE Ch. 3.5 - Prob. 14WE Ch. 3.5 - Prob. 15WE Ch. 3.5 - Prob. 16WE Ch. 3.5 - Prob. 17WE Ch. 3.5 - Prob. 18WE Ch. 3.5 - Prob. 19WE Ch. 3.5 - Prob. 20WE Ch. 3.5 - Prob. 21WE Ch. 3.5 - Prob. 22WE Ch. 3.5 - Prob. 23WE Ch. 3.5 - Prob. 24WE Ch. 3.5 - Prob. 25WE Ch. 3.5 - Prob. 26WE Ch. 3.5 - Prob. 27WE Ch. 3.5 - Prob. 28WE Ch. 3.5 - Prob. 29WE Ch. 3.5 - Prob. 30WE Ch. 3.5 - Prob. 31WE Ch. 3.5 - Prob. 32WE Ch. 3.5 - Prob. 33WE Ch. 3.5 - Prob. 34WE Ch. 3.5 - Prob. 35WE Ch. 3.5 - Prob. 36WE Ch. 3.5 - Prob. 37WE Ch. 3.5 - Prob. 38WE Ch. 3.5 - Prob. 39WE Ch. 3.5 - Prob. 40WE Ch. 3.5 - Prob. 41WE Ch. 3.5 - Prob. 42WE Ch. 3.5 - Prob. 43WE Ch. 3.5 - Prob. 44WE Ch. 3.5 - Prob. 45WE Ch. 3.5 - Prob. 46WE Ch. 3.5 - Prob. 47WE Ch. 3.5 - Prob. 48WE Ch. 3.5 - Prob. 1P Ch. 3.5 - Prob. 2P Ch. 3.5 - Prob. 3P Ch. 3.5 - Prob. 4P Ch. 3.5 - Prob. 5P Ch. 3.5 - Prob. 6P Ch. 3.5 - Prob. 7P Ch. 3.5 - Prob. 8P Ch. 3.5 - Prob. 9P Ch. 3.5 - Prob. 10P Ch. 3.5 - Prob. 11P Ch. 3.5 - Prob. 12P Ch. 3.5 - Prob. 13P Ch. 3.5 - Prob. 14P Ch. 3.5 - Prob. 15P Ch. 3.5 - Prob. 16P Ch. 3.5 - Prob. 17P Ch. 3.5 - Prob. 18P Ch. 3.5 - Prob. 19P Ch. 3.5 - Prob. 20P Ch. 3.5 - Prob. 1MRE Ch. 3.5 - Prob. 2MRE Ch. 3.5 - Prob. 3MRE Ch. 3.5 - Prob. 4MRE Ch. 3.5 - Prob. 5MRE Ch. 3.5 - Prob. 6MRE Ch. 3.5 - Prob. 7MRE Ch. 3.5 - Prob. 8MRE Ch. 3.5 - Prob. 9MRE Ch. 3.5 - Prob. 10MRE Ch. 3.5 - Prob. 11MRE Ch. 3.5 - Prob. 12MRE Ch. 3.5 - Prob. 1CE Ch. 3.5 - Prob. 2CE Ch. 3.5 - Prob. 3CE Ch. 3.5 - Prob. 4CE Ch. 3.5 - Prob. 5CE Ch. 3.5 - Prob. 6CE Ch. 3.5 - Prob. 1ST Ch. 3.5 - Prob. 2ST Ch. 3.5 - Prob. 3ST Ch. 3.5 - Prob. 4ST Ch. 3.6 - Prob. 1OE Ch. 3.6 - Prob. 2OE Ch. 3.6 - Prob. 3OE Ch. 3.6 - Prob. 1P Ch. 3.6 - Prob. 2P Ch. 3.6 - Prob. 3P Ch. 3.6 - Prob. 4P Ch. 3.6 - Prob. 5P Ch. 3.6 - Prob. 6P Ch. 3.6 - Prob. 7P Ch. 3.6 - Prob. 8P Ch. 3.6 - Prob. 9P Ch. 3.6 - Prob. 10P Ch. 3.6 - Prob. 11P Ch. 3.6 - Prob. 12P Ch. 3.6 - Prob. 13P Ch. 3.6 - Prob. 14P Ch. 3.6 - Prob. 15P Ch. 3.6 - Prob. 16P Ch. 3.6 - Prob. 17P Ch. 3.6 - Prob. 18P Ch. 3.6 - Prob. 19P Ch. 3.6 - Prob. 20P Ch. 3.6 - Prob. 1MRE Ch. 3.6 - Prob. 2MRE Ch. 3.6 - Prob. 3MRE Ch. 3.6 - Prob. 4MRE Ch. 3.6 - Prob. 5MRE Ch. 3.6 - Prob. 6MRE Ch. 3.6 - Prob. 7MRE Ch. 3.6 - Prob. 8MRE Ch. 3.6 - Prob. 9MRE Ch. 3.6 - Prob. 10MRE Ch. 3.6 - Prob. 11MRE Ch. 3.6 - Prob. 12MRE Ch. 3.7 - Prob. 1OE Ch. 3.7 - Prob. 2OE Ch. 3.7 - Prob. 1P Ch. 3.7 - Prob. 2P Ch. 3.7 - Prob. 3P Ch. 3.7 - Prob. 4P Ch. 3.7 - 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