The measures of two sides of a triangle are 7 and 11. Determine the range of values for the 3rd side of the triangle.
In a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Let's consider the two given sides of lengths 7 and 11.
To find the range of values for the third side, we need to determine the smallest and largest possible values.
The smallest possible value occurs when the two given sides are placed end to end, forming a line segment. In this case, the third side would have a length of:
11 - 7 = 4
The largest possible value occurs when the two given sides are placed as far apart as possible. In this case, the third side would have a length of:
11 + 7 = 18
Therefore, the range of values for the third side of the triangle is from 4 to 18.