Question 109469
ABCD is a parllelogram,AE perpendicular to DC and CF 
perpendicular to AD. If AB=16cm,AE=8cm and CF=10cm,find AD 
<pre><font size = 5 face = "book antiqua" color = "darkblue"><b>

{{{drawing(400,240,-2,27,-2,17, 
line(0,0,16,0), line(16,0,25.992,8),
line(25.992,8,19.742,15.8062475), line(19.742,15.8062475,9.992,8),
line(0,0,9.992,8), line(9.992,8,25.992,8),
line(0,8,0,0), line(0,8,9.992,8),
locate(0,-.5,A),locate(16,-.5,B),locate(26.5,8.6,C), 
locate(9.5,9.5,D), locate(19.7,17.1,F),locate(0,9.4,E) 
) }}} 




Angle CDF = Angle ADE because they are opposite angles formed 
by two intersecting lines CE and AF

Angle CFD = Angle AED = 90° because AE perpendicular to 
DC and CF perpendicular to AD. 

Triangle CDF is similar to triangle ADE because they have
two angles with the same measure.  

{{{(CD)/(CF)}}} = {{{(AD)/(AE)}}} because of corresponding 
sides of similar triangles are proportional. 

CD = AB = 16cm because they are opposite sides of a parallelogram

Since CD = 16cm , CF = 10cm, AE = 8cm, the above proportion 
becomes:

{{{16/10}}} = {{{(AD)/8}}}

Cross-multiplying,

{{{10(AD)}}} = {{{16*8}}}

{{{10(AD)}}} = {{{128}}}

{{{AD}}} = {{{128/10}}}

{{{AD}}} = {{{12.8cm}}}

Edwin</pre>