Question

in the diagram, $wz = \sqrt{26}$. what is the perimeter of parallelogram $wxyz$? $w(-2,4)$, $x(2,4)$, $z(-3,-1)$, $y(1,-1)$ $\bigcirc$ $2\sqrt{26} + 2$ units $\bigcirc$ $2\sqrt{26} + 4$ units $\bigcirc$ $2\sqrt{26} + 6$ units $\bigcirc$ $2\sqrt{26} + 8$ units

Explanation:

Step1: Calculate length of WX

Use distance formula for $W(-2,4)$ and $X(2,4)$:
$\text{WX} = \sqrt{(2 - (-2))^2 + (4 - 4)^2} = \sqrt{4^2 + 0^2} = 4$

Step2: Recall parallelogram perimeter rule

Perimeter = $2\times(\text{WZ} + \text{WX})$

Step3: Substitute known values

$\text{Perimeter} = 2\times(\sqrt{26} + 4) = 2\sqrt{26} + 8$

Answer:

$2\sqrt{26} + 8$ units