1st Edition

ISBN: 9780618800766

Author: Ron Larson, Lee Stiff, Laurie Boswell, Timothy Kanold

Publisher: Houghton Mifflin-High School

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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 18E

To determine

To find the length of the sides of the triangle and classify it by its side lengths.

Expert Solution & Answer

Answer to Problem 18E

The length of the sides of the triangle are 12 millimeters,6 millimeters and 11 millimeters respectively.

The triangle is scalene triangle.

Explanation of Solution

Given information:

Perimeter of the triangle is given as 29 millimeters

Length of first side is twice the length of the second side of the triangle

Length of the third side is 5 more than the length of the second side of the triangle

Calculation:

Perimeter of the triangle is 29 millimeters

Let the length of second side of the triangle be x

First side of the length is twice the length of the second side,

So can be written it as 2x

Third side of the length is 5 more than the length of the second side,

So can be written it as 5+x

To find the length of all the sides ,add all the sides together.

Hence, can be written it as-

2x+x+5+x=29

Now, add all the x together

4x+5=29

Subtract 5 from both the sides

4x+5−5=29−5

This gives-

4x=24

Now divide both sides by 4

4x4=244

This gives us −

x=6

So the length of the second side of the triangle is 6 millimeters

To find the length of the first side of the triangle-

As known it is 2x. So , multiply 2 times with 6

2×6=12

Hence, length of the second side of the triangle is 12 millimeters

To find the length of the third side of the triangle-

As known it is 5 more than the length of the second side, so will add 5 more to 6

5+6=11

Hence, length of the third side of the triangle is 11 millimeters

Conclusion- The length of the sides of the triangle are 12 millimeters,6 millimeters and 11 millimeters respectively.

Since, all the three sides of the triangle are not the same it is a scalene triangle.

Chapter 10.1, Problem 17E

Chapter 10.1, Problem 19E

Chapter 10 Solutions

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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