Answer: The correct option is (D) 21.
Step-by-step explanation: Given that the point P is an incenter of ΔXYZ. Also, PY = 35 and JY = 28.
We are to find the length of LP.
Since PJ is perpendicular to teh side YZ, so the triangle PJY will be a right-angled triangle with PY as the hypotenuse.
Using Pythagoras theorem in triangle PJY, we have
[tex]PY^2=PJ^2+YJ^2\\\\\Rightarrow PJ^2=PY^2-YJ^2\\\\\Rightarrow PJ^2=35^2-28^2\\\\\Rightarrow PJ^2=441\\\\\Rightarrow PJ=21[/tex]
Since the distance from the incenter of a triangle to all the three sides are equal, so we get
LP = PJ = 21 units.
Option (D) is CORRECT.
