SOLUTION: I need help with a proof that states : Given right triangle RST, angle S as the right angle, RS perpendicular to ST, SW perpendicular to RT as an altitude. PROVE: (ST)^2 = (T

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Question 1021936: I need help with a proof that states :
Given right triangle RST, angle S as the right angle, RS perpendicular to ST, SW perpendicular to RT as an altitude.
PROVE: (ST)^2 = (TW)(TR)

Found 2 solutions by robertb, ikleyn:
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
According to your specifications, triangle STW would be similar to RTS, and hence corresponding sides would be proportional. It follows then that
ST%2FTW+=+TR%2FST.
After cross-multiplication, the equation would be %28ST%29%5E2+=+%28TW%29%28TR%29.



Answer by ikleyn(52879) About Me  (Show Source):
You can put this solution on YOUR website!
.
I need help with a proof that states :
Given right triangle RST, angle S as the right angle, RS perpendicular to ST, SW perpendicular to RT as an altitude.
PROVE: (ST)^2 = (TW)(TR)
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For two different and detailed proofs see the lessons
    - Arithmetic mean and geometric mean inequality - Geometric interpretations
    - Problems on similarity for right-angled triangles
in this site.