   Chapter 5.4, Problem 42E 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

Prove that if ( a , b , c ) is a Pythagorean triple and n is a natural number, the ( n a , n b , n c ) is also a Pythagorean triple.

To determine

To Find:

Proof of (na,nb,nc) is a Pythagorean triple.

Explanation

Given (a,b,c) is a Pythagorean triple then

From the Pythagorean Theorem,

c2=a2+b2.

Then to prove (na,nb,nc) is a Pythagorean triple,

(nc)2=n2c2      =n2(a2+b2)      =n2

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