Mathematics

Problem

\triangle XYZ

, points

M

and

N

lie on

XY

and

XZ

respectively such that

MN \parallel YZ

. Points

P

XM

and

Q

XN

are chosen with

PQ \parallel MN

. If

XY = 18\,\text{cm}

XZ = 24\,\text{cm}

XM = 6\,\text{cm}

XN = 8\,\text{cm}

XP = 3\,\text{cm}

and

YZ = 21\,\text{cm}

, determine the length of

PQ