Mathematics

Problem

In triangle

XYZ

, points

L

M

and

N

are the midpoints of sides

XY

XZ

and

YZ

respectively. a. (i) Prove that quadrilateral

YLMN

is a parallelogram. b. (ii) Show that the area of quadrilateral

YLMN

is exactly half the area of triangle

XYZ

. c. (iii) If

XY = 8\,\text{cm}

XZ = 10\,\text{cm}

and

YZ = 12\,\text{cm}

, find the perimeter of quadrilateral

YLMN