Mathematics

Mathematics

Problem

In

\triangle XYZ

, points

M

and

N

lie on

XY

and

XZ

respectively so that

MN\parallel YZ

. Inside

\triangle XMN

, another line

PQ

is drawn parallel to

MN

meeting

XM

at

P

and

XN

at

Q

. The following data are available:

XM = 6\,\text{cm}

,

MY = 9\,\text{cm}

,

XQ = 4\,\text{cm}

,

QN = 2\,\text{cm}

. a. (i) Determine the lengths of

XN

and

XY

. b. (ii) Calculate

XP

and

PM

. c. (iii) If

YZ = 24\,\text{cm}

, find the length of

PQ

.

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