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 two points \((x_1,y_1)\) and \((x_2,y_2)\) \(d=\vert x_2 - x_1\vert\) (since \(y_1 = y_2 = 4\) for \(W(-2,4)\) and \(X(2,4)\)).
\(WX=\vert2-(-2)\vert=\vert2 + 2\vert = 4\)

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:
\(P=2\sqrt{26}+2\times4=2\sqrt{26}+8\)

Answer:

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