ANSWER
18
EXPLANATION
We are given that the centroid of the triangle is point Q.
The centroid of a triangle is the point where the three medians of the triangle intersect.
This means that KP, JN and LM are medians.
We have that KQ is 12.
According to the median theorem of triangles, the distance between the centroid and the vertex of a particular median is 2/3 of the total length of the median.
This menas that:
KQ = 2/3 * KP
=> 12 = 2/3 * KP
Multiply both sides by 3/2:
=> KP = 12 * 3/2
KP = 18
That is the value of KP
