Mathematics

Problem

\triangle PQR

, points

S

and

T

are on

PQ

and

PR

respectively with

ST \parallel QR

. Points

U

PS

and

V

PT

are chosen such that

UV \parallel ST

. If

PU = 2\,\text{cm}

US = 3\,\text{cm}

SQ = 7\,\text{cm}

and

TR = 9\,\text{cm}

, calculate the length of

PV