SOLUTION: If the lengths of two sides of a triangle are 6 and 7, which of the following could be the length of the third side? I. 1 II. 5 III. 15

Algebra ->  Triangles -> SOLUTION: If the lengths of two sides of a triangle are 6 and 7, which of the following could be the length of the third side? I. 1 II. 5 III. 15      Log On


   

Question 978668: If the lengths of two sides of a triangle are 6 and 7, which of the following could be the length of the third side?

I. 1
II. 5
III. 15
Found 2 solutions by jim_thompson5910, MathLover1:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If x is the missing third side, then

7-6 < x < 7+6

1 < x < 13

So the third side must be between 1 and 13 units. It cannot equal 1 and it cannot equal 13.

The only answer that fits in this interval is II. 5 which is the final answer. The other values are outside of this interval.

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

recall, the sum of the length of any two sides on a triangle is greater than the length of third side
so, if the lengths of two sides of a triangle are 6 and 7,the length of third side is less than 6%2B7=13
and the third side must be between 1 and 13 units
It cannot equal 1 and it cannot equal 13.
The only answer that fits in this interval is II. 5