SOLUTION: Given right triangle ABCABC with altitude \overline{BD}BD drawn to hypotenuse \overline{AC}AC. If AD=9AD=9 and BD=3,BD=3, what is the length of \overline{DC}?DC?

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: Given right triangle ABCABC with altitude \overline{BD}BD drawn to hypotenuse \overline{AC}AC. If AD=9AD=9 and BD=3,BD=3, what is the length of \overline{DC}?DC?      Log On


   



Question 1203446: Given right triangle ABCABC with altitude \overline{BD}BD drawn to hypotenuse \overline{AC}AC. If AD=9AD=9 and BD=3,BD=3, what is the length of \overline{DC}?DC?
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.
Given right triangle ABC with altitude BD drawn to hypotenuse AC.
If AD=9 and BD=3, what is the length of DC?
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If in a right angled triangle ABC, the altitude h = BD from the right angle B
to the hypotenuse AC divides the hypotenuse by segments of the length x and y,
then

    h%5E2 = x*y.    (1)


It is the general formula and the general statement/fact from Euclidean geometry.


In our case  h = BD = 3,  x = AD = 9, and the problem asks about y = DC.


From formula (1),   y = h%5E2%2Fx = 3%5E2%2F9 = 9%2F9 = 1.


ANSWER.  DC = 1.

Solved.


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