Question

P is the incenter of ΔXYZ. If PY = 35 and JY = 28, find LP.

Answer 1

Answer:21

Step-by-step explanation:

Answer 2

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

$PY^2=PJ^2+YJ^2\\\\\Rightarrow PJ^2=PY^2-YJ^2\\\\\Rightarrow PJ^2=35^2-28^2\\\\\Rightarrow PJ^2=441\\\\\Rightarrow PJ=21$

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.