Given right triangle ABCwith altitude BD drawn to hypotenuse AC. If AD=4 and DC=8, what is the length of BD? (Note: the figure is not drawn to scale.)
What is the length of BD?
Hello Guest!
Euclid's theorem of height says
\(h^2 = q \times p\)
so
\(\overline{BD}^2=\overline{AD}\times \overline{CD}\\ \overline{BD}^2=4\cdot 8\\ \overline{BD}=\sqrt{32}=\sqrt{2\cdot 16}\)
\(\overline{BD}=4\sqrt{2}=5.657\)
The length of BD is 5.657
!