## Geometry: Common Core (15th Edition)

$a = 22$ $AD = 18.5$ $AB = 23.6$ $BC = 18.5$ $CD = 23.6$
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: $CD = 23.6$