Second question
From the information given, P is the centroid of the triangle. The centroid theorem states that the centroid of the triangle is at 2/3 of the distance from the vertex to the midpoint of the sides. Considering the given triangle, it means that in triangle LMN,
LP = 2/3BL
LP + BP = BL
Given that BP = 3, then
LP + 3 = BL
2/3LB + 3 = LB
BL - 2/3BL = 3
1/3BL = 3
Multiply both sides by 3. We have
3 * 1/3LB = 3 * 3
BL = 9
LP = 2/3 * 9
LP = 6
Option A is correct
