Answer
$HK=15$
Work Step by Step
Similar figures have congruent corresponding angles. Thus...
$m\angle D=m\angle L=90^{\circ}$
or, Angle D is a right angle creating right triangle $HLK$
Similar figures have proportional corresponding sides.
$\frac{AD}{HL}=\frac{DC}{LK}$
Substitute in the appropriate values...
$\frac{8}{12}=\frac{6}{x}$
Cross multiply...
$6(12)=8(x)$
$72=8x$
Divide both sides by 8...
$x=9$ or $LK=9$
We now have the lengths of two sides of our right triangle. Both lengths are leg lengths. Using Pythagorean Theorem...
$9^{2}+12^{2}=c^{2}$
Simplify...
$81+144=c^{2}$
$225=c^{2}$
Square root both sides...
$c=15$ or $HK=15$
