Question

quadrilaterals wxyz and badc are congruent. in addition, \\( \overline { wx } \cong \overline { dc } \\) and \\( \overline { xy } \cong \overline { bc } \\). if \\( ad = 4 \mathrm { cm } \\) and \\( ab = 6 \mathrm { cm } \\), what is the perimeter of wxyz? 22 cm 24 cm 18 cm 20 cm

Explanation:

Step1: Use the property of congruent quadrilaterals

Since quadrilaterals \(WXYZ\) and \(BADC\) are congruent, their corresponding sides are equal.

Step2: Recall the formula for the perimeter of a quadrilateral

The perimeter \(P\) of a quadrilateral is \(P = AB + BC+CD + DA\). For quadrilateral \(BADC\), \(AB = 6\mathrm{cm}\), \(AD = 4\mathrm{cm}\). Because \(WX\cong DC\) and \(XY\cong BC\), and by the congruence of \(WXYZ\) and \(BADC\), the perimeter of \(WXYZ\) is the same as the perimeter of \(BADC\).
Using the formula \(P=2(AB + AD)\) (since in a quadrilateral with \(AB\) and \(AD\) as adjacent sides and using the congruence - equivalent to a parallelogram - like property from congruence of sides \(WX\cong DC\), \(XY\cong BC\)).
Substitute \(AB = 6\mathrm{cm}\) and \(AD = 4\mathrm{cm}\) into the formula \(P = 2(AB + AD)\).

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Answer:

\(20\mathrm{cm}\)