#### Answer

38.4 inches

#### Work Step by Step

1. We are told that YW is 14.3 inches.
2. Since YX is congruent to YZ, which equals 7.8 inches, YX equals 7.8 inches.
3. Since we found it is a right triangle, we use the Pythagorean theorem to find XW:
$XW = \sqrt{ 7.8^2 + 14.3^2} = 16.3$
Thus:
$P = 16.3 + 7.8 + 14.3 = 38.4$