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?
A) 21.4 B) 22.5 C) 23.8 D) 24.5
Answers
22.5 cm is the length of YZ
Step-by-step explanation:
Given that,
In ║gm MNOP with extension of PM to Z.
OX = 27 cm
XY = 18 cm
A.T.Q.,
In ΔXYN & ΔXOP,
∠YXN = ∠PXO (∵ Interior Angles)
∠NYX = ∠POX (∵ Alternate Interior Angles)
∵ ΔXYN ~ ΔXOP (using Angle-Angle rule)
As we know that,
The ratio of two similar Δ's sides = the ratio of sides corresponding
So,
XY/OX = XN/PX
⇒ 18/27 = XN/PX
∵ XN/PX = 2/3 ...(i)
Now, In ΔPXZ & ΔOXN,
∠PXZ = ∠NXO (∵ Alternate Interior Angles)
∠XZP = ∠XON (∵ Alternate Interior Angles)
∵ ΔPXZ ~ ΔOXN (using AA rule)
The ratio of two similar Δ's sides = the ratio of sides corresponding
⇒ (YZ + YX)/XO = PX/XN
⇒ (YZ + 18)/27 = 3/2 (using equation (i)
⇒ 2 * YZ + 36 = 81
∵ YZ = 22.5
Thus, the length of side YZ is 22.5 cm
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