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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
= 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 = = = = 1.
ANSWER. DC = 1.
Solved.
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