Final answer:
To find the length of JK, we use the angle bisector theorem. Setting up the equation and solving for x, we find that x = 1.76. Substituting the value of x back into the equation, we find that JK = 2.04.
Step-by-step explanation:
To find the length of JK, we need to use the angle bisector theorem. In triangle JKP, the angle bisector PD divides the side JK into two segments, JD and DK. The angle bisector theorem states that the ratio of the lengths of the two segments is equal to the ratio of the lengths of the two sides that form the angle.
So, we can set up the equation:
JD / DK = JP / KP
Substituting the given values:
x / (4x - 5) = 12 / 14
Solving for x:
14x = 12(4x - 5)
14x = 48x - 60
60 = 48x - 14x
60 = 34x
x = 60 / 34
x = 1.76
Now that we have the value of x, we can find the length of JK:
JK = 4x - 5
JK = 4(1.76) - 5
JK = 7.04 - 5
JK = 2.04