Answer
$AB = 17$ cm
$BC = 31$ cm
$CD = 17$ cm
$DA = 31$ cm
Work Step by Step
Since $\square ABCD$ is a parallelogram, this means that $AB = CD$ and also $BC = DA$.
$CD = 2x + 3$
$BC = 5x - 4$
$Perimeter = 96$ cm
1. Solve for$ x$
Perimeter $= (2 \times CD) + (2 \times BC)$
$96 = 2(2x+3) + 2(5x-4)$
$96 = (4x+6) + (10x - 8)$
$96 = 14x - 2$
$98 = 14x$
$x = \frac{98}{14}$
$x = 7$ cm
2. Substitute the $x$ value into the $CD$ and $BC$ equations (Remember that $AB = CD$ and $BC = DA$)
$AB = 2x + 3$
$AB = 2(7) + 3$
$AB = 14 + 3$
$AB = 17$ cm
$BC = 5x - 4$
$BC = 5(7) -4$
$BC = 35 -4 $
$BC = 31$ cm
$CD = 2x + 3$
$CD = 2(7) + 3$
$CD = 14 + 3$
$CD= 17$ cm
$DA = 5x - 4$
$DA = 5(7) -4$
$DA = 35 -4 $
$DA = 31$ cm
