Mathematics

Problem

\triangle PQR

, two distinct lines are drawn parallel to

QR

. The first line

ST

meets

PQ

S

and

PR

T

. The second line

UV

meets

PQ

U

(between

P

and

S

) and

PR

V

. The following measurements are known:

PS = 4\,\text{cm}

SQ = 8\,\text{cm}

PT = 5\,\text{cm}

TR = 10\,\text{cm}

and

PU = 3\,\text{cm}

. Answer the following: a. (i) Find the lengths of

PQ

and

PR

. b. (ii) Calculate the length of

PV

. c. (iii) Determine the ratio

UV : QR