AMC10 2027 - Self-practice Set 2 Question 14

Question 14

The area of $\triangle EBD$ is one third of the area of the $3$-$4$-$5$ triangle $ABC.$ Segment $DE$ is perpendicular to segment $AB.$ What is $BD?$

Question illustration

$\dfrac{4}{3} $
$\sqrt{5} $
$\dfrac{9}{4} $
$\dfrac{4\sqrt{3}}{3} $
$\dfrac{5}{2} $