Applying the Triangle Midsegment Theorem, we find x = 18, y = 14, and z = 11. The perimeter of the triangle is 43 units, calculated by summing the sides. This theorem simplifies finding midsegment lengths and aids in determining triangle side lengths.
Applying the Triangle Midsegment Theorem, the midsegment 2x is half the length of the parallel side, so x = 18. Similarly, for the other midsegments, y - 2 = 12 yields y = 14, and z + 8 = 19 gives z = 11.
Now, knowing x, y, and z, we can find the perimeter of the triangle by summing all sides: 18 + 14 + 11 = 43. Thus, x = 18, y = 14, z = 11, and the perimeter is 43 units.