Chapter 5.4, Problem 13E

### Elementary Geometry For College St...

7th Edition
Alexander + 2 others
ISBN: 9781337614085

Chapter
Section

### Elementary Geometry For College St...

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

# Determine the type of triangle represented if the lengths of its sides are:a) a =   4 ,         b =   3   a n d     c   =   5 b) a =   4 ,         b =   5   a n d     c   =   6 c) a = 2 ,         b =   a n d     c   =   d) a =   3 ,       b =   8   a n d     c   =   15

To determine

(a)

To Find:

Type of the triangle.

Explanation

Given a=4,Â b=3Â andÂ c=5,

Let a, b and c are the lengths of the three sides of the triangle, with c is the longest side, then

From the triangle theorems,

1. If the square of the length of the longest side is greater than the sum of square of the lengths of other two sides then the triangle is Obtuse.

c2>a2+b2

2. If the square of the length of the longest side is less than the sum of square of the lengths of other two sides then the triangle is Acute.

c2<a2+b2

3. If the square of the length of the longest side is equal to the sum of square of the lengths of other two sides then the triangle is Right triangle

To determine

(b)

To Find:

Type of the triangle.

To determine

(c)

To Find:

Type of the triangle.

To determine

(d)

To Find:

Type of the triangle.

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