SOLUTION: ABCD is a parllelogram,AE perpendicular to DC and CF perpendicular to AD.If AB=16cm,AE=8cm and CF=10cm,find AD

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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
Answer by Edwin McCravy(6936) About Me  (Show Source):
You can put this solution on YOUR website!
ABCD is a parllelogram,AE perpendicular to DC and CF
perpendicular to AD. If AB=16cm,AE=8cm and CF=10cm,find AD 


drawing%28400%2C240%2C-2%2C27%2C-2%2C17%2C+%0D%0Aline%280%2C0%2C16%2C0%29%2C+line%2816%2C0%2C25.992%2C8%29%2C%0D%0Aline%2825.992%2C8%2C19.742%2C15.8062475%29%2C+line%2819.742%2C15.8062475%2C9.992%2C8%29%2C%0D%0Aline%280%2C0%2C9.992%2C8%29%2C+line%289.992%2C8%2C25.992%2C8%29%2C%0D%0Aline%280%2C8%2C0%2C0%29%2C+line%280%2C8%2C9.992%2C8%29%2C%0D%0Alocate%280%2C-.5%2CA%29%2Clocate%2816%2C-.5%2CB%29%2Clocate%2826.5%2C8.6%2CC%29%2C+%0D%0Alocate%289.5%2C9.5%2CD%29%2C+locate%2819.7%2C17.1%2CF%29%2Clocate%280%2C9.4%2CE%29+%0D%0A%29+ 




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.  

%28CD%29%2F%28CF%29 = %28AD%29%2F%28AE%29 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%2F10 = %28AD%29%2F8

Cross-multiplying,

10%28AD%29 = 16%2A8

10%28AD%29 = 128

AD = 128%2F10

AD = 12.8cm

Edwin