directions: if each quadrilateral below is a rectangle
1.

Question

Accepted Answer

# Explanation:
## Step1: Use rectangle properties
In a rectangle, opposite sides are equal. So $VW = YX = 31$, $WX=VY = 19$.
## Step2: Use Pythagorean theorem for diagonals
For rectangle $VYWX$, diagonals $VX$ and $YW$ are equal. By Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $a = 19$, $b = 31$, and $c$ is the length of the diagonal.
$$
\begin{align*}
VX&=\sqrt{19^{2}+31^{2}}\
&=\sqrt{361 + 961}\
&=\sqrt{1322}\
\end{align*}
$$
Since $Z$ is the mid - point of the diagonal $VX$ (diagonals of a rectangle bisect each other), $ZX=\frac{1}{2}VX$.
$$
\begin{align*}
VX&=\sqrt{19^{2}+31^{2}}=\sqrt{361 + 961}=\sqrt{1322}\approx36.36\
ZX&=\frac{\sqrt{1322}}{2}\approx18.18\
YW&=VX=\sqrt{1322}\approx36.36
\end{align*}
$$

# Answer:
$VW = 31$, $WX = 19$, $YW=\sqrt{19^{2}+31^{2}}=\sqrt{1322}\approx36.36$, $ZX=\frac{\sqrt{1322}}{2}\approx18.18$, $VX=\sqrt{19^{2}+31^{2}}=\sqrt{1322}\approx36.36$

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QUESTION IMAGE

Question

Explanation:

Step1: Use rectangle properties

Step2: Use Pythagorean theorem for diagonals

Answer: