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Two sides of scalene Triangle ABC measure 3 centimeters and 5 centimeters. How many different whole centimeter lengths are possible for the third side?

 Oct 14, 2019
 #1
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Let the unknown side = S

 

By the triangle inequality

 

S < 3 + 5

S < 8

 

S + 3 > 5

S > 2

 

And

 

S + 5 < 3

S > -2

 

But  taking the most  restrictive interval

 

2 < S < 8

 

But since the triangle is scalene.....then the possible lengths for S  are  4, 6, and 7 (cm)

 

cool cool cool

 Oct 14, 2019
edited by CPhill  Oct 14, 2019
 #2
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 CPhill i think you meant S+5>3

Guest Oct 15, 2019

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