MathDB

In rectangle

ABCD

, points

F

and

G

lie on

\overline{AB}

so that AF \equal{} FG \equal{} GB and

E

is the midpoint of

\overline{DC}

. Also,

\overline{AC}

intersects

\overline{EF}

H

and

\overline{EG}

J

. The area of the rectangle

ABCD

70

. Find the area of triangle

EHJ

. [asy] size(180); pair A, B, C, D, E, F, G, H, J; A = origin; real length = 6; real width = 3.5; B = length*dir(0); C = (length, width); D = width*dir(90); F = length/3*dir(0); G = 2*length/3*dir(0); E = (length/2, width); H = extension(A, C, E, F); J = extension(A, C, E, G);
draw(A--B--C--D--cycle); draw(G--E--F); draw(A--C);
label("

A

", A, dir(180)); label("

D

", D, dir(180)); label("

B

", B, dir(0)); label("

C

", C, dir(0)); label("

F

", F, dir(270)); label("

E

", E, dir(90)); label("

G

", G, dir(270)); label("

H

", H, dir(140)); label("

J

", J, dir(340)); [/asy]

\displaystyle <span class='latex-bold'>(A)</span> \ \frac {5}{2} \qquad <span class='latex-bold'>(B)</span> \ \frac {35}{12} \qquad <span class='latex-bold'>(C)</span> \ 3 \qquad <span class='latex-bold'>(D)</span> \ \frac {7}{2} \qquad <span class='latex-bold'>(E)</span> \ \frac {35}{8}

Problem Statement