In a triangle with side lengths 5, 10 and x, what is the sum of all possible integral values of x?
+128406 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
