Question

in the diagram, ( wz = sqrt{26} ). what is the perimeter of parallelogram ( wxyz )? ( 2sqrt{26}+2 ) units ( 2sqrt{26}+4 ) units ( 2sqrt{26}+6 ) units ( 2sqrt{26}+8 ) units

Explanation:

Step1: Find the length of \( XY \)

In a parallelogram \( WXYZ \), \( WZ = XY=\sqrt{26} \) (opposite sides of a parallelogram are equal).

Step2: Find the length of \( WX \)

Use the distance formula for two points \( (x_1,y_1) \) and \( (x_2,y_2) \): \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \). For \( W(-2,4) \) and \( X(2,4) \), \( x_1=-2,y_1 = 4,x_2=2,y_2 = 4 \). Then \( WX=\sqrt{(2-(-2))^2+(4 - 4)^2}=\sqrt{(2 + 2)^2+0^2}=\sqrt{16}=4 \). Since \( WX=YZ = 4 \) (opposite sides of a parallelogram are equal).

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