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Two side lengths of a triangle are 11 and 17. What is the longest possible integer length of the third side of the triangle?


Dont know where to start

 Jan 21, 2021
 #1
avatar+267 
+3

use the good ol' pythagorean theorem

 

a^2+b^2=c^2

 

11^2+17^2=410

 

x^2=410

 

sqrt410 (can't be simplified any further) 

 Jan 21, 2021
 #3
avatar-11 
-1

I tried this when I did it, and it wasn't right, but Cphill gave a simple answer which used triangle inequality. Great answer though, I can see why you got that

jeffthememeguy  Jan 21, 2021
 #2
avatar+116126 
+2

Got to  be careful here.....we might not necessarily  have a right triangle

 

In general.....The sum of any two sides of a triangle is greater than the remaining side  (this is known as the trinagle inequality)

 

So

 

11+ 17   =  28

 

So   the remaining side   must  be  <  28 =    27

 

cool cool cool

 Jan 21, 2021
 #4
avatar-11 
-1

Thanks so much! I'll definitely do a little bit more research on triangle inequality 

jeffthememeguy  Jan 21, 2021

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