Algebra: Structure And Method, Book 1
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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Question
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Chapter 3.5, Problem 13P
To determine

To find: the length of the longest side of triangle

Expert Solution & Answer
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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=3x16

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

  x+43x=3x163x

Combine like terms on both sides

  2x+4=16

Subtract 4 on both sides of the equation

  2x+44=164

Combine like terms on both sides of the equation

  2x=20

Divide -2 on both sides of the equation

  2x2=202

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 Solutions

Algebra: Structure And Method, Book 1

Ch. 3.1 - Prob. 11OECh. 3.1 - Prob. 12OECh. 3.1 - Prob. 13OECh. 3.1 - Prob. 14OECh. 3.1 - Prob. 15OECh. 3.1 - Prob. 16OECh. 3.1 - Prob. 17OECh. 3.1 - Prob. 18OECh. 3.1 - Prob. 19OECh. 3.1 - Prob. 20OECh. 3.1 - Prob. 21OECh. 3.1 - Prob. 1WECh. 3.1 - Prob. 2WECh. 3.1 - Prob. 3WECh. 3.1 - Prob. 4WECh. 3.1 - Prob. 5WECh. 3.1 - Prob. 6WECh. 3.1 - Prob. 7WECh. 3.1 - Prob. 8WECh. 3.1 - Prob. 9WECh. 3.1 - Prob. 10WECh. 3.1 - Prob. 11WECh. 3.1 - Prob. 12WECh. 3.1 - Prob. 13WECh. 3.1 - Prob. 14WECh. 3.1 - Prob. 15WECh. 3.1 - Prob. 16WECh. 3.1 - Prob. 17WECh. 3.1 - Prob. 18WECh. 3.1 - Prob. 19WECh. 3.1 - Prob. 20WECh. 3.1 - Prob. 21WECh. 3.1 - Prob. 22WECh. 3.1 - Prob. 23WECh. 3.1 - Prob. 24WECh. 3.1 - Prob. 25WECh. 3.1 - Prob. 26WECh. 3.1 - Prob. 27WECh. 3.1 - Prob. 28WECh. 3.1 - Prob. 29WECh. 3.1 - Prob. 30WECh. 3.1 - Prob. 31WECh. 3.1 - Prob. 32WECh. 3.1 - Prob. 33WECh. 3.1 - Prob. 34WECh. 3.1 - Prob. 35WECh. 3.1 - Prob. 36WECh. 3.1 - Prob. 37WECh. 3.1 - Prob. 38WECh. 3.1 - Prob. 39WECh. 3.1 - 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Prob. 2WECh. 3.5 - Prob. 3WECh. 3.5 - Prob. 4WECh. 3.5 - Prob. 5WECh. 3.5 - Prob. 6WECh. 3.5 - Prob. 7WECh. 3.5 - Prob. 8WECh. 3.5 - Prob. 9WECh. 3.5 - Prob. 10WECh. 3.5 - Prob. 11WECh. 3.5 - Prob. 12WECh. 3.5 - Prob. 13WECh. 3.5 - Prob. 14WECh. 3.5 - Prob. 15WECh. 3.5 - Prob. 16WECh. 3.5 - Prob. 17WECh. 3.5 - Prob. 18WECh. 3.5 - Prob. 19WECh. 3.5 - Prob. 20WECh. 3.5 - Prob. 21WECh. 3.5 - Prob. 22WECh. 3.5 - Prob. 23WECh. 3.5 - Prob. 24WECh. 3.5 - Prob. 25WECh. 3.5 - Prob. 26WECh. 3.5 - Prob. 27WECh. 3.5 - Prob. 28WECh. 3.5 - Prob. 29WECh. 3.5 - Prob. 30WECh. 3.5 - Prob. 31WECh. 3.5 - Prob. 32WECh. 3.5 - Prob. 33WECh. 3.5 - Prob. 34WECh. 3.5 - Prob. 35WECh. 3.5 - Prob. 36WECh. 3.5 - Prob. 37WECh. 3.5 - Prob. 38WECh. 3.5 - Prob. 39WECh. 3.5 - Prob. 40WECh. 3.5 - Prob. 41WECh. 3.5 - Prob. 42WECh. 3.5 - Prob. 43WECh. 3.5 - Prob. 44WECh. 3.5 - Prob. 45WECh. 3.5 - Prob. 46WECh. 3.5 - Prob. 47WECh. 3.5 - Prob. 48WECh. 3.5 - Prob. 1PCh. 3.5 - Prob. 2PCh. 3.5 - Prob. 3PCh. 3.5 - Prob. 4PCh. 3.5 - Prob. 5PCh. 3.5 - Prob. 6PCh. 3.5 - Prob. 7PCh. 3.5 - Prob. 8PCh. 3.5 - Prob. 9PCh. 3.5 - Prob. 10PCh. 3.5 - Prob. 11PCh. 3.5 - Prob. 12PCh. 3.5 - Prob. 13PCh. 3.5 - Prob. 14PCh. 3.5 - Prob. 15PCh. 3.5 - Prob. 16PCh. 3.5 - Prob. 17PCh. 3.5 - Prob. 18PCh. 3.5 - Prob. 19PCh. 3.5 - Prob. 20PCh. 3.5 - Prob. 1MRECh. 3.5 - Prob. 2MRECh. 3.5 - Prob. 3MRECh. 3.5 - Prob. 4MRECh. 3.5 - Prob. 5MRECh. 3.5 - Prob. 6MRECh. 3.5 - Prob. 7MRECh. 3.5 - Prob. 8MRECh. 3.5 - Prob. 9MRECh. 3.5 - Prob. 10MRECh. 3.5 - Prob. 11MRECh. 3.5 - Prob. 12MRECh. 3.5 - Prob. 1CECh. 3.5 - Prob. 2CECh. 3.5 - Prob. 3CECh. 3.5 - Prob. 4CECh. 3.5 - Prob. 5CECh. 3.5 - Prob. 6CECh. 3.5 - Prob. 1STCh. 3.5 - Prob. 2STCh. 3.5 - Prob. 3STCh. 3.5 - Prob. 4STCh. 3.6 - Prob. 1OECh. 3.6 - Prob. 2OECh. 3.6 - Prob. 3OECh. 3.6 - Prob. 1PCh. 3.6 - Prob. 2PCh. 3.6 - Prob. 3PCh. 3.6 - Prob. 4PCh. 3.6 - Prob. 5PCh. 3.6 - Prob. 6PCh. 3.6 - Prob. 7PCh. 3.6 - Prob. 8PCh. 3.6 - Prob. 9PCh. 3.6 - Prob. 10PCh. 3.6 - Prob. 11PCh. 3.6 - Prob. 12PCh. 3.6 - 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