Question

given that the quadrilateral ( wxyz ) is a parallelogram, ( overline{wt}=23 mathrm{~cm} ) and ( overline{xt}=12 mathrm{~cm} ), what is ( overline{xz} )?

Explanation:

Step1: Recall the property of parallelogram diagonals

In a parallelogram, the diagonals bisect each other. So, if \(WXYZ\) is a parallelogram, then \(XT = TZ\).

Step2: Calculate the length of \(XZ\)

Since \(XT = 12\) cm and \(XZ=XT + TZ\), and \(XT = TZ\) (diagonals bisect each other in a parallelogram), we have \(XZ = 2\times XT\).
Substitute \(XT = 12\) cm into the formula: \(XZ=2\times12\).

Answer:

\(24\)