Mathematics

Problem

\triangle XYZ

, points

P

XY

and

Q

XZ

are such that

XP = 3\,\text{cm}

PY = 4.5\,\text{cm}

XQ = 5\,\text{cm}

and

QZ = 7.5\,\text{cm}

. (i) Show that

PQ \parallel YZ

. (ii) If

XY

is produced to a point

R

so that

YR = XP

, calculate

XR