Answer:

Apologies for the confusion in the previous responses. Let's reevaluate the given figure to find the length of AB.

In the figure, we have triangle PAC and line segment CD. To find the length of AB, we need to use the concept of similar triangles.

Since triangle PAC and triangle ABC are similar, we can set up the following proportion:

AB/AC = PC/PA

Substituting the given values, we have:

AB/AC = 16/14

Cross-multiplying, we get:

AB * 14 = AC * 16

To find the length of AB, we need to determine the value of AC. We can use the fact that the sum of the lengths of the sides of a triangle is equal to the perimeter.

In triangle PAC, we have:

PA + AC + PC = perimeter

14 + AC + 16 = perimeter

Since CD is given as 18 cm, we can substitute AC with (PC - CD) in the equation:

14 + (PC - CD) + 16 = perimeter

14 + (16 - 18) + 16 = perimeter

14 + (-2) + 16 = perimeter

28 = perimeter

Now, we can solve for AC:

AC = perimeter - PA - PC

AC = 28 - 14 - 16

AC = -2 cm

Since AC is negative, it means that the triangle is not possible with the given measurements. Therefore, we cannot determine the length of AB in this case.

Apologies for the confusion once again.