In quadrilateral WXYZ, XQ and ZP are perpendicular to WY such that XQ = ZP. The diagonals ZX and WY intersect at point O. If OX = 12 cm, find the length of ZX in cm.

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Given quadrilateral WXYZ, with XQ and ZP perpendicular to WY and XQ = ZP, the diagonals ZX and WY intersect at O. We know OX = 12 cm.

Since XQ and ZP are equal perpendiculars from points X and Z to WY, triangles formed by these perpendiculars are congruent or symmetric with respect to WY.

The intersection O divides diagonal ZX such that OX = OZ (because of the equal perpendiculars and symmetry). Given OX = 12 cm, OZ = 12 cm.

Therefore, the entire diagonal ZX = OX + OZ = 12 + 12 = 24 cm.

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