SOLUTION: if the sides of a triangle have lengths of x, 2x+1, and 10, which of the following is a possible value for x? A. 1 B. 3 C. 6 D. 9 E. 11

Algebra ->  Triangles -> SOLUTION: if the sides of a triangle have lengths of x, 2x+1, and 10, which of the following is a possible value for x? A. 1 B. 3 C. 6 D. 9 E. 11      Log On


   



Question 478269: if the sides of a triangle have lengths of x, 2x+1, and 10, which of the following is a possible value for x?
A. 1
B. 3
C. 6
D. 9
E. 11

Found 2 solutions by cleomenius, MathLover1:
Answer by cleomenius(959) About Me  (Show Source):
You can put this solution on YOUR website!
The Triangle Inequality Theorem states that the sum of the lengths of any 2 sides of a triangle must be greater than the third side.
This eliminates 1, 3, 9, and 11.
The only possible answer listed is 6.
Cleomenius.

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

Theorem: The sum of the lengths of any two sides of a triangle must be greater than the third side.
x%2B+2x%2B1%3E10
3x%3E10-1
3x%3E9
x%3E3
or
x%2B+10%3E2x%2B1
x-2x%3E1-10
-x%3E-9
x%3C9...........

or
2x%2B1%2B+10%3Ex%2B1
2x%2B11%3Ex%2B1
2x-x%3E1-11
x%3E-10
since x%3E3 and x%3C9, the answer is:
C. 6