2005 iTest Problems/Problem 18
Revision as of 20:39, 13 October 2025 by Mathloveryeah (talk | contribs) (Created page with "==Problem== If the four sides of a quadrilateral are <math>2, 3, 6</math>, and <math>x</math>, find the sum of all possible integral values for <math>x</math>. ==Solution 1==...")
Problem
If the four sides of a quadrilateral are 
, and 
, find the sum of all possible integral values for .
Solution 1
The sum of the 3 smallest sides must be greater than the largest side. Thus, must satisfy the following two inequalities: 
and 
. Solving, we find (respectively) that 
and 
. Therefore, our answer is 
.
See Also
| 2005 iTest (Problems, Answer Key) | ||
| Preceded by: Problem 17 |
Followed by: Problem 19 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 • 51 • 52 • 53 • 54 • 55 • 56 • 57 • 58 • 59 • 60 • TB1 • TB2 • TB3 • TB4 | ||
