A triangle has two sides of length 6 and 9. what value could the length of the third side be? check all that apply.
This must pass the Triangle Inequality....thus....
6 + missing side > 9
missing side > 3
6 + 9 > missing side
15 > missing side
3 < missing side < 15
So....A, B , C and F are possible answers
There is a specific theorem thats could help, its called the triangle inequality therom. So you cannot have the third side of your triangle must be greater than the difference of the two other sides. And also smaller than the sum of the two sides so.
If you subtract 9 and 6 you get 3. So E.2 Is off the table. Since it is lower.
If you add 9 and 6 you get 15. So D.15 is off the table. Since it is equal to or greater than the combination of 9 and 6.
So the answers you have left are A.10, B.7, C.4, F.12. Since they are in between the diference of (9-6) and the addition of (9+6).
Hope this helps ;P
Imagine the angle between the two sides to be 1o - the 9" side would extend 3" past the 6" side. Since the answers are rounded, the third side could be 3"
Now consider that angle to be 179o - the third side would be 9" plus 6" which is 15"
Mentally view the 9" side swinging in an arc from the 1o position to the 179o position. The third side can be any length between the extremes.
so the answers are between 3" and 15" - therefore 10, 7, 4, 15, and 12.