Question

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

Explanation:

Step1: Recall the property of congruent quadrilaterals

Since quadrilaterals \(WXYZ\) and \(BADC\) are congruent, their corresponding sides are equal. So, \(WX = DC\), \(XY=BC\), \(YZ = AD\), \(ZW=AB\).

Step2: Calculate the perimeter of \(BADC\)

The perimeter of a quadrilateral is the sum of its side - lengths. For quadrilateral \(BADC\), \(P_{BADC}=AB + BC+CD + DA\). Given \(AD = 4\mathrm{cm}\) and \(AB = 6\mathrm{cm}\). Also, \(P_{WXYZ}=P_{BADC}\) (because \(WXYZ\cong BADC\)).
Since \(P = AB + BC + CD+DA\), and \(BC = XY\), \(CD = WX\), \(DA = YZ\), \(AB = ZW\). Substituting the values: \(P=(AB + AD)+(BC + CD)\). Since \(BC + CD=AB + AD\) (because \(WX\cong DC\) and \(XY\cong BC\), and \(AB = ZW\), \(AD = YZ\)), \(P = 2(AB + AD)\).
Substitute \(AB = 6\mathrm{cm}\) and \(AD = 4\mathrm{cm}\) into the formula: \(P=2(6 + 4)\).

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Answer:

\(20\mathrm{cm}\) (the second option)