If Z is the centroid of ∆LMN, WZ=4,ZN=14, and ZY = 10, find each missing measure

ZM = 8 units, WM = 12 units, XZ = 7 units, XN = 21 units and LZ = 20 units.  

  Properties of the centroid of a triangle,

From the triangle given in the picture,

Z is the centroid of ΔLMN.

Centroid divides the medians XN, LY and MW in the ratio of 2 : 1.

a). ZM : ZW = 2 : 1

    ZM = 8 units

b). WM = ZM + ZW

            = 8 + 4

            = 12 units

c). ZN : XZ = 2 : 1

    XZ = 7 units

d). XN = XZ + ZN

          = 7 + 14

          = 21 units

e). LZ : ZY = 2 : 1

    LZ = 20 units

    Therefore, ZM = 8 units, WM = 12 units, XZ = 7 units, XN = 21 units and LZ = 20 units.  

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ZM = 8

WM = 12

XZ = 7

XN = 21

LZ = 20

Step-by-step explanation:

The centroid of a triangle is the point of intersection of the midpoint of the each of the three sides of a triangle. The centroid of a triangle is located inside the triangle and it is known as the center of gravity.

The centroid theorem for a triangle states that the centroid of a triangle is located at 2/3 of the distance from the vertex of the triangle of the middle of the opposite side.

ZM = (2/3)WM (centroid theorem)

Therefore: WZ = (1/3)WM

WM = 3WZ = 3 * 4 = 12

ZM = (2/3) * WM = 2/3 * 12 = 8

ZN = (2/3)XN (centroid theorem)

XN = (3/2)ZN = 3/2 * 14 = 21

XN = 21

XZ + ZN = XN

XZ + 14 = 21

XZ = 7

LZ = (2/3)LY (centroid theorem)

Therefore: ZY = (1/3)LY

LY = 3ZY = 3 * 10 = 30

LZ = (2/3) * LY = 2/3 * 30 = 20

26?

step-by-step explanation:

11

step-by-step explanation:

32.50-7.50=25

225/25=11