12th Edition

ISBN: 9780358403685

Author: Larson

Publisher: HM CC

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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 10.1, Problem 26E

To determine

TO-DETERMINE if the given side lengths form a triangle using triangle inequality theorem.

Expert Solution & Answer

Answer to Problem 26E

Option C forms a triangle using the triangle inequality theorem.

Explanation of Solution

Given information:

The triangle inequality theorem states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Three options are given along with their sides-

a. 4,5,104,5,9 c. 4,5,7

Calculation:

As per the theorem,

x+y>zx+z>yy+z>x

Now check for all the three options given

Option a- 4,5,10

Let x=4,y=5,z=10

x+y>z gives 4+5>10

Now add and check-

9>10 which is incorrect.

So, option a cannot form a triangle using the inequality theorem.

Option b- 4,5,9

Let x=4,y=5,z=9

x+y>z gives 4+5>9

Now add and check-

9>10 which is incorrect.

So , option b cannot form a triangle using the inequality theorem.

Option c- 4,5,7

Let x=4,y=5,z=7

x+y>z Gives 4+5>7

Now add and check-

9>7 which is correct

Now with the other two equations as well

x+z>y Gives 4+7>5

Now add and check-

11>5 which is correct

y+z>x Gives 5+7>7

Now add and check-

12>5 which is correct

So, option c fulfills the inequality theorem.

Conclusion- Since option c fulfils the sum of the lengths of any two sides of a triangle which is greater than the length of the third side.

Hence, option c forms a triangle using inequality theorem.

Chapter 10.1, Problem 25E

Chapter 10.1, Problem 27E

Chapter 10 Solutions

EBK PRE-ALGEBRA

Ch. 10.1 - Prob. 1C Ch. 10.1 - Prob. 2C Ch. 10.1 - Prob. 3C Ch. 10.1 - Prob. 1E Ch. 10.1 - Prob. 2E Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - Prob. 5E Ch. 10.1 - Prob. 6E Ch. 10.1 - Prob. 7E

Ch. 10.1 - Prob. 8E Ch. 10.1 - Prob. 9E Ch. 10.1 - Prob. 10E Ch. 10.1 - Prob. 11E Ch. 10.1 - Prob. 12E Ch. 10.1 - Prob. 13E Ch. 10.1 - Prob. 14E Ch. 10.1 - Prob. 15E Ch. 10.1 - Prob. 16E Ch. 10.1 - Prob. 17E Ch. 10.1 - Prob. 18E Ch. 10.1 - Prob. 19E Ch. 10.1 - Prob. 20E Ch. 10.1 - Prob. 21E Ch. 10.1 - Prob. 22E Ch. 10.1 - Prob. 23E Ch. 10.1 - Prob. 24E Ch. 10.1 - Prob. 25E Ch. 10.1 - Prob. 26E Ch. 10.1 - Prob. 27E Ch. 10.1 - Prob. 28E Ch. 10.1 - Prob. 29E Ch. 10.1 - Prob. 30E Ch. 10.1 - Prob. 31E Ch. 10.1 - Prob. 32E Ch. 10.2 - Prob. 1C Ch. 10.2 - Prob. 2C Ch. 10.2 - Prob. 3C Ch. 10.2 - Prob. 1E Ch. 10.2 - Prob. 2E Ch. 10.2 - Prob. 3E Ch. 10.2 - Prob. 4E Ch. 10.2 - Prob. 5E Ch. 10.2 - Prob. 6E Ch. 10.2 - Prob. 7E Ch. 10.2 - Prob. 8E Ch. 10.2 - Prob. 9E Ch. 10.2 - Prob. 10E Ch. 10.2 - Prob. 11E Ch. 10.2 - Prob. 12E Ch. 10.2 - Prob. 13E Ch. 10.2 - Prob. 14E Ch. 10.2 - Prob. 15E Ch. 10.2 - Prob. 16E Ch. 10.2 - Prob. 17E Ch. 10.2 - Prob. 18E Ch. 10.2 - Prob. 19E Ch. 10.2 - Prob. 20E Ch. 10.2 - 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