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 w(-2,4) x(2,4) z(-3,-1) y(1,-1)

Explanation:

Step1: Find the length of WX

Since W(-2,4) and X(2,4) have the same y - coordinate, the length of WX is calculated using the distance formula for points with the same y - value: $d=\vert x_2 - x_1\vert$. Here, $x_1=-2$ and $x_2 = 2$, so $WX=\vert2-(-2)\vert=4$.

Step2: Recall the property of a parallelogram

In a parallelogram, opposite sides are equal. So $WZ = XY=\sqrt{26}$ and $WX = ZY = 4$.

Step3: Calculate the perimeter

The perimeter $P$ of a parallelogram is $P = 2(WZ)+2(WX)$. Substitute $WZ=\sqrt{26}$ and $WX = 4$ into the formula: $P=2\sqrt{26}+2\times4=2\sqrt{26}+8$.

Answer:

$2\sqrt{26}+8$ units