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? \\(\bigcirc\\) 18 cm \\(\bigcirc\\) 20 cm \\(\bigcirc\\) 22 cm \\(\bigcirc\\) 24 cm

Explanation:

Step1: Recall congruent quadrilaterals property

Congruent quadrilaterals have equal corresponding sides. So, perimeter of \(WXYZ\) = perimeter of \(BADC\).

Step2: Analyze sides of \(BADC\)

In quadrilateral \(BADC\), from the congruence and given \( \overline{WX} \cong \overline{DC}\), \( \overline{XY} \cong \overline{BC}\), also \(AB\) and \(AD\) are sides. Since \(WXYZ \cong BADC\), corresponding sides: \(WX = DC\), \(XY = BC\), \(YZ = AD\), \(ZW = AB\).

Step3: Calculate perimeter of \(BADC\)

Perimeter of \(BADC = AB + BC + CD + DA\). From congruence, \(BC = XY\), \(CD = WX\), but also, since \(WXYZ \cong BADC\), the sides of \(BADC\) are \(AB = 6\) cm, \(AD = 4\) cm, and since it's a quadrilateral (assuming it's a parallelogram - like structure from congruence of sides \(WX \cong DC\) and \(XY \cong BC\), so opposite sides equal), so \(BC = AD = 4\) cm, \(CD = AB = 6\) cm. Wait, actually, more simply, perimeter of \(BADC = 2\times(AB + AD)\) (since in congruent quadrilaterals with \(WX \cong DC\) and \(XY \cong BC\), so \(WXYZ\) has sides equal to \(BADC\)'s sides, so \(WXYZ\) has two sides equal to \(AB\) and \(AD\) (since \(WX \cong DC\), \(XY \cong BC\), \(YZ \cong AD\), \(ZW \cong AB\)). So perimeter of \(WXYZ = 2\times(AB + AD)\).
Substitute \(AB = 6\) cm, \(AD = 4\) cm: \(2\times(6 + 4)=2\times10 = 20\) cm.

Answer:

20 cm