The measure of two sides of a triangle are 7 and 11. Determine the range of values for the third side of the triangle
____ < n < ____
In a triangle, the length of any side must be less than the sum of the lengths of the other two sides.
So, for the third side of the triangle to be valid, it must satisfy the following condition:
7 + 11 > third side
This simplifies to:
18 > third side
Therefore, the third side of the triangle must be less than 18.
On the other hand, the length of the third side must be greater than the absolute value of the difference between the lengths of the other two sides:
|7 - 11| < third side
This simplifies to:
4 < third side
Combining the two conditions, the range of values for the third side is:
4 < third side < 18