Question

if $xv = 27 - 2x$ and $vz = 3x + 2$, find $vz$ and $xz$.
$vz =$
$xz =$
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Explanation:

Step1: Set segments equal (diagonals bisect)

$27-2x=3x+2$

Step2: Solve for $x$

$27-2=3x+2x \implies 25=5x \implies x=5$

Step3: Calculate $VZ$

$VZ=3(5)+2=15+2=17$

Step4: Calculate $XZ$

$XZ=XV+VZ=2VZ=2\times17=34$

Answer:

$VZ=17$
$XZ=34$