Answer
$a = 22$
$AD = 18.5$
$AB = 23.6$
$BC = 18.5$
$CD = 23.6$
Work Step by Step
The diagram is that of a parallelogram.
Opposite sides of a parallelogram are congruent. We see that $\overline{AD}$ and $\overline{BC}$ are opposite sides.
Let's set $AD$ and $BC$ equal to one another so we can solve for $a$:
$AD = BC$
Let's plug in what we know:
$a - 3.5 = 18.5$
Add $3.5$ to each side of the equation to isolate constants on one side:
$a = 22$
Now that we have the value for $x$, we can plug it into the expression to find the lengths of the sides of this parallelogram. We need to find the other three sides.
$AB = 2a - 20.4$
Plug in $22$ for $a$:
$AB = 2(22) - 20.4$
Multiply first, according to order of operations:
$AB = 44 - 20.4$
Subtract to solve:
$AB = 23.6$
Let's find $BC$ next:
$BC = a - 3.5$
Plug in $22$ for $a$:
$BC = 22 - 3.5$
Subtract to solve:
$BC = 18.5$
Let's find $CD$:
$CD = a + 1.6$
Plug in $22$ for $a$:
$CD = 22 + 1.6$
Add to solve:
$CD = 23.6$
