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In rectangle $ABCD$, shown here, $\overline{CE}$ is perpendicular to $\overline{BD}$. If $BC = \sqrt 3$ and $DC = 3$, what is $CE$?

 

:P thanks to whoever answers it 

 Feb 3, 2021
 #1
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We know $CE \times DB = CB \times DC$ because area of triangles

DB is 6 cuz DBC is 30 60 90

$6 \times CE = 3\sqrt{3}$

$CE = \sqrt{3}/2$

 Feb 3, 2021
 #2
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tan  BDC    =   sqrt 3    /  3    =    1 /sqrt 3)

So  BDC   =  30°

 

Then CE  is opposite a 30°  angle in right triangle DEC

 

So...it has  half the  length  of  the hypotenuse  DC   = (1/2) 3 =    3/2

 

 

cool cool cool

 Feb 3, 2021

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