Can you help me find the area with steps?

Question

anonymous · Answer

Find the area of a right tri. , given that the altitude to the hypotenuse separates the hypotenuse into segments of lengths 9cm and 16cm.

So, I draw it this way..
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hartnn · Answer

there are 2 ways to find the length of that altitude, say 'h'
Geometric Mean, 
h^2 = 9*16

or, 
using similar triangles. 
(does this question belong to similar triangles topic ? if no, you can directly use the geometric mean formula)

anonymous · Answer

Yes, we did tackle that but I'm not sure where this belong since my teacher always mix things up.
What do you think is the best connection to this prob? :|

hartnn · Answer

ok, then have you ever heard that altitute is geometric mean ?
if not then this probably is similar triangles topic

anonymous · Answer

hmm. i'l choose similar triangles then..
how shall I do it?

hartnn · Answer

let the altitude be AD 
we need to prove triangle ABD ~ triangle CAD

hartnn · Answer

which angles are obviously equal ? (hint : right angles in both triangles)

anonymous · Answer

<BAD ~ <CAD?

hartnn · Answer

no...neither of those angles are right angle

hartnn · Answer

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