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In a triangle with side lengths 5, 10 and x, what is the sum of all possible integral values of x?

 May 15, 2022
 #1
avatar+14084 
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The sum of all possible integral values of x is 14 - 5 = 9. Thanks BuilderBoi!

laugh  !

 May 15, 2022
edited by asinus  May 16, 2022
 #2
avatar+2448 
+1

The triangle inequality states that the sum of the 2 smallest sides must be greater than the largest side. 

 

This means that x can be anywhere from 6 to 14, because \(6 + 5 > 10\) and \(5+10>14\).

 

Now, we need to find the sum of all the numbers between 6 and 14. 

 

Can you take it from here?

 May 15, 2022

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