Question

in the diagram, wz=√26. what is the perimeter of parallelogram wxyz? 2√26 + 2 units 2√26 + 4 units 2√26 + 6 units 2√26 + 8 units

Explanation:

Step1: Find the length of \( WX \)

Use the distance formula for points \( W(-2,4) \) and \( X(2,4) \).
Since \( y - \)coordinates are the same (\( y_1=y_2 = 4 \)), \( WX=\vert x_2 - x_1\vert=\vert2-(-2)\vert = 4\) units.

Step2: Recall the property of a parallelogram

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

Step3: Calculate the perimeter

The perimeter \( P\) of a parallelogram is \( P = 2(WZ+WX)\).
Substitute \( WZ=\sqrt{26}\) and \( WX = 4\) into the formula: \( P=2\sqrt{26}+8\).

Answer:

\( 2\sqrt{26}+8 \) units