Triangle - What is the length of the hypotenuse? Triangle ABC has a right angle at corner C. It has a height from C to a point D on side |AB|. If |CD|=5 and |AD|=7 then what is the length of the hypotenuse? (|AB|=?)

Correct Answer: 74/7 

I have tried solving the question above by the help of the law of cosines and sines, pythagoras theorm and uniform triangles but without much success. I always tend to get to many unknown variables. Thanks in advance.
Draw a picture.  You just need similar triangles.  $ABC,ACD,$ and $CBD$ are similar.  $\frac {BD}{DC}=\frac {CD}{AD}=\frac 57$ so $BD=\frac {25}7$ and $AB=AD+BD=7+\frac {25}7=\frac {74}7$
Draw a picture.  You just need similar triangles.  $ABC,ACD,$ and $CBD$ are similar.  $\frac {BD}{DC}=\frac {CD}{AD}=\frac 57$ so $BD=\frac {25}7$ and $AB=AD+BD=7+\frac {25}7=\frac {74}7$