   Chapter 8.2, Problem 45E 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

For Exercises 45 and 46, use this information: Let a, b, and c be the integer lengths of the sides of a triangle. If the area of the triangle is also an integer, then (a, b, c) is known as a Heron triple.Which of these are Heron triples? a) (5, 6, 7) b) (13, 14, 15)

To determine

(a)

To Check:

The area of the triangle value is integer or not and conclude the provided information satisfies Heron triple or not.

Explanation

Formula Used:

Heron’s Formula: If the three sides of a triangle have lengths a,b and c then the area A of the triangle is given by A=s(s-a)(s-b)(s-c),

where the semiperimeter of the triangle is s=12(a+b+c).

Calculation:

Consider the triple (5, 6, 7). That is, a=5,b=6and c=7.

s=125+6+7=9

Applying

To determine

(b)

To Check:

The area of the triangle value is integer or not and conclude the provided information satisfies Heron triple or not.

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