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
We know $CE \times DB = CB \times DC$ because area of triangles
DB is 6 cuz DBC is 30 60 90
$6 \times CE = 3\sqrt{3}$
$CE = \sqrt{3}/2$
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
