MathDB

The area of

\triangle EBD

is one third of the area of

3-4-5

\triangle ABC

. Segment

DE

is perpendicular to segment

AB

. What is

BD

?
[asy] unitsize(10mm); defaultpen(linewidth(.8pt)+fontsize(10pt)); dotfactor=4; pair A=(0,0), B=(5,0), C=(1.8,2.4), D=(5-4sqrt(3)/3,0), E=(5-4sqrt(3)/3,sqrt(3)); pair[] ps={A,B,C,D,E}; draw(A--B--C--cycle); draw(E--D); draw(rightanglemark(E,D,B)); dot(ps); label("

A

",A,SW); label("

B

",B,SE); label("

C

",C,N); label("

D

",D,S); label("

E

",E,NE); label("

3

",midpoint(A--C),NW); label("

4

",midpoint(C--B),NE); label("

5

",midpoint(A--B),SW);[/asy]

<span class='latex-bold'>(A)</span>\ \frac{4}{3} \qquad <span class='latex-bold'>(B)</span>\ \sqrt{5} \qquad <span class='latex-bold'>(C)</span>\ \frac{9}{4} \qquad <span class='latex-bold'>(D)</span>\ \frac{4\sqrt{3}}{3} \qquad <span class='latex-bold'>(E)</span>\ \frac{5}{2}

Problem Statement