SOLUTION: If x is an integer and 2 < x < 7, how many different triangle are there with sides of lengths 2,7 and x? This is a multiple choice question with the following answers One, Two,

Algebra ->  Triangles -> SOLUTION: If x is an integer and 2 < x < 7, how many different triangle are there with sides of lengths 2,7 and x? This is a multiple choice question with the following answers One, Two,      Log On


   

Question 937012: If x is an integer and 2 < x < 7, how many different triangle are there with sides of lengths 2,7 and x?
This is a multiple choice question with the following answers
One, Two, Three, Four and Five.
The answer given was One.
But the way i understood is x could be of any value of the following 3, 4, 5 and 6. So I selected FOUR. Can you please help me on how the answer is One?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

given:
2%3Cx%3C+7
Now, a triangle must be such that the sum of any+two sides must be greater than the third side.
So, immediately, we are down to 3, 4, 5, 6 under given conditions.
If x+=+3 then 2%2B3+%3C+7 --- not a triangle!
if x+=+4 then 2+%2B+4+%3C+7 -- not a triangle
if x+=+5 then 2+%2B+5+=+7 -- not a triangle
if x = 6 then 2%2B+6+%3E+7 -- triangle
so, 1 value of x works; so, answer is one