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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?

 Dec 3, 2020
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We need to observe  the triangle inequality rule that says   that  the  sum of the lengths of any two sides of a triangle  is greater than the  length of the  remaining side

 

So we have

 

5 + 10  >  x

15 >  x

So....the  largest integral value of  x =  14

 

And

 

5 + x  >  10

x >  10-5

x > 5

So....the smallest integral value of x =  6

 

Sum of   intergers from  6 - 14  inclusive  =

 

[first integer + last ineger ]  * [ number of terms ]   / 2   =

 

[6 + 14]  [ 14 - 6 + 1 ]   / 2   =

 

[20 ] [ 9 ] / 2  =

 

(20/2)  * 9  =

 

10 ( 9)  =

 

90

 

 

cool cool cool

 Dec 3, 2020

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