Question

Point O is the centroid of triangle STU. The internal line segments are the medians of the triangle. The length of median PU is 81 millimeters.
The length of segment PO is ____ millimeters, and the length of segment OU is ____ millimeters.

Answer 1

The length of segment PO is _27_ millimeters, and the length of segment OU is _54_ millimeters.

Justification:

Centroid → intersection point of medians.

And we know that,

Centroid divides median in ratio of 2:1

So, OU/PO = 2/1

• OU = 2PO ...[1]

Now,

PU = 81mm

• PO + OU = 81
• PO + 2PO = 81
• 3PO = 81
• PO = 81/3 = 27mm.

And OU = 2PO

• OU = (2 × 27)mm
• OU = 54mm.

Answer 2

Answer: PO is 27 mm and OU is 54 mm

Step-by-step explanation: