WXYZ is a quadrilateral in which XQ and ZP are perpendicular to WY such that XQ = ZP. Diagonals ZX and WY intersect each other at point O. If OX = 12 cm, then find the value of ZX (in cm).
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 24.
XQ ⊥ WY and ZP ⊥ WY
XQ = ZP and OX = 12 cm
In triangles XQO and ZPO,
XQ = ZP
∠XQO = ∠ZPO = 90°
∠QOX = ∠POZ (vertically opposite angles)
So, XQO ≅ ZPO [ASA Rule]
Then, OX = OZ
ZX = OX + OZ = 12 + 12 = 24 cm
Therefore, the value of ZX is 24 cm.