Question

in the diagram, wz=$\sqrt{26}$. what is the perimeter of parallelogram wxyz? 2$\sqrt{26}$ + 2 units 2$\sqrt{26}$ + 4 units 2$\sqrt{26}$ + 6 units 2$\sqrt{26}$ + 8 units

Explanation:

Step1: Find the length of \( WX \)

Use the distance formula for horizontal line (since \( y - \)coordinates of \( W(-2,4) \) and \( X(2,4) \) are same). \( d=\vert x_2 - x_1\vert\).
\( WX=\vert2-(-2)\vert=\vert2 + 2\vert = 4\)

Step2: Recall the property of parallelogram

In a parallelogram \( WXYZ\), \( WZ = XY=\sqrt{26}\) and \( WX = YZ = 4\)

Step3: Calculate the perimeter

Perimeter of parallelogram \( P=2(WZ+WX)\)
Substitute \( WZ=\sqrt{26}\) and \( WX = 4\)
\( P=2\sqrt{26}+2\times4=2\sqrt{26}+8\)

Answer:

\( 2\sqrt{26}+8\) units (the fourth option)