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
(diagram: coordinate grid with points w(-2,4), x(2,4), z(-3,-1), y(1,-1))

Explanation:

Step1: Find length of WX

In a parallelogram, opposite sides are equal. For points W(-2,4) and X(2,4), the distance (length of WX) is calculated by the difference in x - coordinates (since y - coordinates are same). So, \( WX=\vert2 - (-2)\vert=\vert4\vert = 4\).

Step2: Recall perimeter formula for parallelogram

The perimeter \( P\) of a parallelogram is given by \( P = 2(a + b)\), where \( a\) and \( b\) are the lengths of adjacent sides. Here, one side is \( WZ=\sqrt{26}\) and the adjacent side is \( WX = 4\).

Step3: Calculate the perimeter

Substitute \( a=\sqrt{26}\) and \( b = 4\) into the perimeter formula: \( P=2(\sqrt{26}+4)=2\sqrt{26}+8\) units.

Answer:

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