2005 iTest Problems/Problem 18

Problem

If the four sides of a quadrilateral are $2, 3, 6$ , and $x$ , find the sum of all possible integral values for $x$ .

Solution 1

The sum of the 3 smallest sides must be greater than the largest side. Thus, $x$ must satisfy the following two inequalities: $2+3+x>6$ and $2+3+6>x$ . Solving, we find (respectively) that $x>1$ and $x<11$ . Therefore, our answer is $2+3+4+5+6+7+8+9+10=\boxed{54}$ .

2005 iTest (Problems, Answer Key)
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2005 iTest Problems/Problem 18

Problem

Solution 1

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