Questions: If each quadrilateral below is a rectangle

Transcript text: If each quadrilateral below is a rectangle

Solution

Solution Steps

Step 1: Find WX

The given rectangle has VY = 19 and YX = 31. Since it is a rectangle, VY = WX and YX = VW. Therefore, WX = 19.

Step 2: Find VW

VW = YX = 31.

Step 3: Find YW

YW is a diagonal of the rectangle. In rectangle VWXY, triangle VYW is a right triangle. Using Pythagorean theorem, $YW^2 = VY^2 + VW^2 = 19^2 + 31^2 = 361 + 961 = 1322$. So, $YW = \sqrt{1322}$.

Step 4: Find ZX

ZX is a diagonal, so ZX = VY. Also diagonals bisect each other in a rectangle. Therefore, $ZX = YW = \sqrt{1322}$.

Step 5: Find VX

VX is a diagonal. $VX^2 = WX^2 + VW^2 = 19^2 + 31^2 = 361 + 961 = 1322$. $VX = \sqrt{1322}$.

Final Answer

$VW = 31$ $WX = 19$ $YW = \sqrt{1322}$ $ZX = \sqrt{1322}$ $VX = \sqrt{1322}$

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