Algebra 2
Algebra 2
1st Edition
ISBN: 9780078884825
Author: McGraw-Hill/Glencoe
Publisher: Glencoe/McGraw-Hill School Pub Co
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Chapter 3, Problem 19PT

a.

To determine

To calculate: The lengths of the sides of the trapezoid.

a.

Expert Solution
Check Mark

Answer to Problem 19PT

The length of shorter base is 11 inches, longer base is 27 inches and length of congruent legs is 10 inches.

Explanation of Solution

Given information:

In an isosceles trapezoid a denote the measure of shorter base, c denote the measure of longer base and b denote the measure of congruent legs,

The perimeter is 58 inches. The average of bases is 19 inches and longer base is twice the leg plus 7.

Calculation:

Consider the provided information thatin an isosceles trapezoid a denote the measure of shorter base, c denote the measure of longer base and b denote the measure of congruent legs,

The perimeter is 58 inches. The average of bases is 19 inches and longer base is twice the leg plus 7.

Therefore, equations formed are,

  a+b+c=58a+c2=19c=2b+7

Rewrite the above system as,

  a+2b+c=58a+c=38c=2b+7

Substitute a+c=38 in a+2b+c=58 .

  2b+38=58b=10

Substitute b=10 in c=2b+7 ,

  c=2(10)+7c=27

Substitute c=27 in a+c=38

  a+27=38a=11

Thus, length of shorter base is 11 inches, longer base is 27 inches and length of congruent legs is 10 inches.

b.

To determine

To calculate: The area of trapezoid.

b.

Expert Solution
Check Mark

Answer to Problem 19PT

The area is 114square inches.

Explanation of Solution

Given information:

The length of shorter base is 11 inches, longer base is 27 inches and length of congruent legs is 10 inches.

Calculation:

Consider the provided information thatlength of shorter base is 11 inches, longer base is 27 inches and length of congruent legs is 10 inches.

The area of trapezoid is 12( sum of parallel sides)( height) .

Sum of parallel sides is sum of shorter and longer base.

Consider the graphical representation of trapezoid

  Algebra 2, Chapter 3, Problem 19PT

The value of d is,

  d+d+11=272d=16d=8

Use the Pythagoras theorem to evaluate the value of h .

  82+h2=102h2=100−64h2=36h=6

The area of trapezoid is,

  12( sum of parallel sides)( height)=12(11+27)6=114 .

Thus, area of trapezoid is 114 square inches.

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Chapter 3, Problem 18PT
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Chapter 3, Problem 1E

Chapter 3 Solutions

Algebra 2

Ch. 3.1 - Prob. 1ACYPCh. 3.1 - Prob. 1BCYPCh. 3.1 - Prob. 2ACYPCh. 3.1 - Prob. 2BCYPCh. 3.1 - Prob. 3CYPCh. 3.1 - Prob. 4ACYPCh. 3.1 - Prob. 4BCYPCh. 3.1 - Prob. 4CCYPCh. 3.1 - Prob. 4DCYPCh. 3.1 - Prob. 1CYU
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Prob. 30HPCh. 3.5 - Prob. 31HPCh. 3.5 - Prob. 32HPCh. 3.5 - Prob. 33HPCh. 3.5 - Prob. 34STPCh. 3.5 - Prob. 35STPCh. 3.5 - Prob. 36STPCh. 3.5 - Prob. 37STPCh. 3.5 - Prob. 38STPCh. 3.5 - Prob. 39SCh. 3.5 - Prob. 40SCh. 3.5 - Prob. 41SCh. 3.5 - Prob. 42SCh. 3 - Prob. 1QCCh. 3 - Prob. 2QCCh. 3 - Prob. 3QCCh. 3 - Prob. 4QCCh. 3 - Prob. 5QCCh. 3 - Prob. 6QCCh. 3 - Prob. 7QCCh. 3 - Prob. 8QCCh. 3 - Prob. 9QCCh. 3 - Prob. 10QCCh. 3 - Prob. 11QCCh. 3 - Prob. 12QCCh. 3 - Prob. 13QCCh. 3 - Prob. 14QCCh. 3 - Prob. 1MCQCh. 3 - Prob. 2MCQCh. 3 - Prob. 3MCQCh. 3 - Prob. 4MCQCh. 3 - Prob. 5MCQCh. 3 - Prob. 6MCQCh. 3 - Prob. 7MCQCh. 3 - Prob. 8MCQCh. 3 - Prob. 9MCQCh. 3 - Prob. 10MCQCh. 3 - Prob. 11MCQCh. 3 - Prob. 12MCQCh. 3 - Prob. 13MCQCh. 3 - Prob. 14MCQCh. 3 - Prob. 15MCQCh. 3 - Prob. 16MCQCh. 3 - Prob. 17MCQCh. 3 - Prob. 18MCQCh. 3 - Prob. 19MCQCh. 3 - Prob. 20MCQCh. 3 - Prob. 21MCQCh. 3 - Prob. 22MCQCh. 3 - Prob. 1SGRCh. 3 - Prob. 2SGRCh. 3 - Prob. 3SGRCh. 3 - Prob. 4SGRCh. 3 - Prob. 5SGRCh. 3 - 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