#### Answer

By definition of a kite we conclude that side BC=DC and BC=DC
P= 2BC+2DC
59.2=4BC+10
49.2=4BC
BC= 12.3

#### Work Step by Step

We can find $BC$:
$P = AB+BC+CD+DA = 59.2$
$AB+BC+BC+AB = 59.2$
$(BC+5)+BC+BC+(BC+5) = 59.2$
$4~BC+10 = 59.2$
$4~BC = 49.2$
$BC = \frac{49.2}{4}$
$BC = 12.3$