SOLUTION: ABC is a right angle triangle ,where angle b= 90 degree . BD drawn perpendicular to AC . AD=9 DC= 16. Find AB

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Question 837675: ABC is a right angle triangle ,where angle b= 90 degree . BD drawn perpendicular to AC . AD=9 DC= 16. Find AB
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!

The altitude BD splits right triangle ABC into right triangles ADB and BCD.
They are all similar right triangles.
The ratio {leg adjacent to angle BAC)/hypotenuse is
AB%2FAC=AB%2F%28AD%2BDC%29 in triangle ABC,
and it is AD%2FAB in triangle ADB.
Since those two triangles are similar, those ratios are the same,
so AB%2F%28AD%2BDC%29=AD%2FAB <--> %28AB%29%5E2=AD%2A%28AD%2BDC%29 .
Substituting numbers,
%28AB%29%5E2=9%289%2B16%29
%28AB%29%5E2=9%2A25
%28AB%29%5E2=3%5E2%2A5%5E2
%28AB%29%5E2=%283%2A5%29%5E2
%28AB%29%5E2=15%5E2
highlight%28AB=15%29