In the given figure, MNOP is a parallelogram. PM is extended to Z. OZ intersects MN and PN at Y and X respectively. If OX = 27 cm and XY = 18 cm, then what is the length (in cm) of YZ ?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2, i.e. 22.5
MNOP is a parallelogram
In △PXO and △NXY
∠PXO = ∠NXY (vertically opposite angle)
∠XPO = ∠XNY (vertically opposite angle)
So, △PXO ~ △NXY
XO/XY = PO/NY
YN/PO = 18/27
MX/PO = 3-2/2 = 1/3
Now in △ZPO:
ZY/ZO = MY/PO = 1/3
ZY/(ZY + 45) = 1/3
ZY = 22.5