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# Given right triangle ABCABC with altitude \overline{BD}BD drawn to hypotenuse \overline{AC}AC. If AB=2AB=2 and AC=4,AC=4

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Given right triangle ABCABC with altitude \overline{BD}BD drawn to hypotenuse \overline{AC}AC. If AB=2AB=2 and AC=4,AC=4, what is the length of \overline{AD}?AD?

May 8, 2021

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Given right triangle ABC with altitude$$\overline{BD}$$ drawn to hypotenuse $$\overline{AC}$$.
If $$\overline{AB}=2$$ and $$\overline{AC}=4$$,
what is the length of $$\overline{AD}$$?

$$\begin{array}{|rcll|} \hline \overline{AB}^2 &=& \overline{AD}\times \overline{AC} \\ 2^2 &=&\overline{AD}\times 4 \\ 4 &=&\overline{AD}\times 4 \\ \mathbf{\overline{AD}} &=& \mathbf{1} \\ \hline \end{array}$$

May 8, 2021