## Elementary Geometry for College Students (6th Edition)

$HK=15$
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 $HK=15$