we have three similar triangles, because each has a right angle and shares an angle. let's write the angles in order: opposite to short leg, long leg, hypotenuse.
cab similar to bad similar to cbd
or as ratios,
ca: ab: cb = ba: ad: bd = cb: bd: cd
we also know
ac = ad + cd
(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd
(ad+cd)/cb=cb/cd
we have cb=6, ad=5 and seek x=cd.
![(5 + x)/6 = 6/x](/tex.php?f=(5 + x)/6 = 6/x)
![x(x+5) = 36](/tex.php?f=x(x+5) = 36)
![x^2 +5x - 36 = 0](/tex.php?f=x^2 +5x - 36 = 0)
![(x+9)(x-4) = 0](/tex.php?f=(x+9)(x-4) = 0)
we reject the negative root and conclude x=4
answer: 4
![If bc = 6 and ad = 5, find dc. a) 4 b) 4.5 c) 7.2](/tpl/images/05/01/aSKUPngOWnr7g4U2.jpg)