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# Geometry

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If altitude CD is $$8 \sqrt{3}$$ centimeters, what is  BD?

Feb 15, 2022

#1
+2444
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This problem is actually simple because it is a 30-60-90 triangle.

Because we know that $$CD = 8\sqrt3$$$$AD$$ must equal $$\sqrt2\times 8\sqrt3 = 8\sqrt6$$

We also know that $$BD$$ must equal to $${8\sqrt3}\over\sqrt2$$, which can be rewritten as $$4\sqrt6$$

This means that $$\color{brown}\boxed{AB=12\sqrt6}$$

Feb 15, 2022
#2
+124594
+1

Note that triangles  ACD ,  CBD  are  similar  and each are 30-60-90 right triangles

And since  AD is opposite a 60° angle it =  sqrt 3 * CD =  sqrt 3 * 8 sqrt 3 =  24

And, by similar triangles, we have the following relationship

DB / DC  = DC / AD

(8sqrt 3)^2  = DB * 24

256 / 24  = DB  = 32 / 3  (cm)

Feb 15, 2022
#3
+2444
+1

I misread the question... DB should be $$4 \sqrt6$$, because $$\triangle{CDB}$$ is a 30-60-90.

Feb 15, 2022