In , points and lie on and respectively so that . Inside , another line is drawn…

MATHEMATICS · Multi-part · CBSE · Mathematics · Triangles · Triangles

Problem

\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

P

and

XN

Q

. The following data are available:

XM = 6\,\text{cm}

MY = 9\,\text{cm}

XQ = 4\,\text{cm}

QN = 2\,\text{cm}

. (i) Determine the lengths of

XN

and

XY

. (ii) Calculate

XP

and

PM

. (iii) If

YZ = 24\,\text{cm}

, find the length of

PQ