Since J, P, and L are the midpoints of KH, HM, and MK, respectively, the values of x, y, and z are as follows;
x = 4.75
y = 6
z = 1
How to find the Centroid of the Triangle?
The centroid theorem states that the centroid of a triangle is located at two-third (2/3) of the distance from the vertex to the midpoint of the (opposite) sides.
The centroid of a triangle simply refers to the point where the three (3) medians of the triangle meet or intersect. By applying the centroid theorem to triangle KHM (ΔKHM);
Side HQ = (2/3)(LH)
y = (2/3)(3 + y)
3y = 2(3 + y)
3y = 6 + 2y
y = 6.
Side KQ = (2/3)(KP)
7 = (2/3)(7 + 2x - 6)
21 = 2(1 + 2x)
10.5 = 1 + 2x
2x = 9.5.
x = 4.75.
Side QM = (2/3)(JM)
4 = (2/3)(2z + 4)
12 = 2(2z + 4)
6 = 2z + 4
2z = 2
z = 1.