14.)
If AB = 13.BC = 6,CD = 2x - 18.
and AD = 4x - 29
find CD.

12

Step-by-step explanation:

13 + 6 + 2x -18 = 4x - 29

19 + 2x -18 = 4x -29

2x + 1 = 4x - 29

30 = 2x

15 = x

CD = 2(15) -18

CD = 30 -18

CD = 12

2

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.

we reject the negative root and conclude x=4

answer: 4