   Chapter 5.CR, Problem 42CR Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Solutions

Chapter
Section Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085
Textbook Problem

Tell whether each set of numbers represents the lengths of the sides of an acute triangle, of an obtuse triangle, of a right triangle, or of no triangle: a) 12, 13, 14 e) 8, 7, 16 b) 11, 5, 18 f) 8, 7, 6 c) 9, 15, 18 g) 9, 13, 8 d) 6, 8, 10 h) 4, 2, 3

To determine

a)

To find:

The set of numbers represents the length of an

 Acute triangle Obtuse triangle Right triangle No triangle
Explanation

Approach:

If a, b and c are the sides of the triangle, then

1) c2<a2+b2, (triangle is acute)

2) c2>a2+b2 (Triangle is obtuse)

3) c2=a2+b2 (Triangle is right)

Given, set of numbers is 12, 13 and 14.

Let us take a=12,b=13 and c=14

Here, greatest side is c

To determine

b)

To find:

The set of numbers represents the length of an

 Acute triangle Obtuse triangle Right triangle No triangle
To determine

c)

To find:

The set of numbers represents the length of an

 Acute triangle Obtuse triangle Right triangle No triangle
To determine

d)

To find:

The set of numbers represents the length of an

 Acute triangle Obtuse triangle Right triangle No triangle
To determine

e)

To find:

The set of numbers represents the length of an

 Acute triangle Obtuse triangle Right triangle No triangle
To determine

f)

To find:

The set of numbers represents the length of an

 Acute triangle Obtuse triangle Right triangle No triangle
To determine

g)

To find:

The set of numbers represents the length of an

 Acute triangle Obtuse triangle Right triangle No triangle
To determine

h)

To find:

The set of numbers represents the length of an

 Acute triangle Obtuse triangle Right triangle No triangle

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