Question

in the diagram, ( zy = wx = 2sqrt{10} ). what is the perimeter of rectangle ( wxyz )?
( sqrt{10} ) units
( 2sqrt{10} ) units
( 6sqrt{10} ) units
( 8sqrt{10} ) units

Explanation:

Step1: Calculate the length of \( WX \)

Given \( WX = 2\sqrt{10} \). Since \( WXYZ \) is a rectangle, \( ZY=WX = 2\sqrt{10} \) and \( WZ = XY \).
Use the distance formula \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \) to find \( WZ \).
For points \( W(-6,6) \) and \( Z(-9,5) \):

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Since \( WZ = XY=\sqrt{10} \)

Step2: Calculate the perimeter of the rectangle

The perimeter formula of a rectangle is \( P=2(l + w) \), where \( l = 2\sqrt{10} \) and \( w=\sqrt{10} \)

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Answer:

\( 6\sqrt{10} \) units