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MATH / In rectangle ABCD, points F and G lie on (AB)¯ so that AF=FG=GB and E is the midpoint of (DC)¯. Also, (AC)¯ intersects (EF)¯ at H and (EG)¯ at J. The area of rectangle ABCD is 70. …

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

In rectangle ABCDABCD, points FF and GG lie on AB¯\overline{AB} so that AF=FG=GBAF = FG = GB and EE is the midpoint of DC¯\overline{DC}. Also, AC¯\overline{AC} intersects EF¯\overline{EF} at HH and EG¯\overline{EG} at JJ. The area of rectangle ABCDABCD is 70. Find the area of triangle EHJEHJ. [asy] pair A,B,C,D,I,F,G,H,J; A=(0,0); B=(9,0); C=(9,5); D=(0,5); F=(3,0); G=(6,0); I=(4.5,5); H=(3.5,1.67); J=(5,3.33); draw(A--B--C--D--cycle); draw(A--C); draw(F--I--G); label("AA",A,W); label("BB",B,E); label("CC",C,E); label("DD",D,W); label("EE",I,N); label("FF",F,S); label("GG",G,S); label("HH",H,NW); label("JJ",J,NE); [/asy]
Plain-text mathematical notation (without MathML)
In rectangle ABCD, points F and G lie on (AB)¯ so that AF=FG=GB and E is the midpoint of (DC)¯. Also, (AC)¯ intersects (EF)¯ at H and (EG)¯ at J. The area of rectangle ABCD is 70. Find the area of triangle EHJ.

[asy]
pair A,B,C,D,I,F,G,H,J;
A=(0,0);
B=(9,0);
C=(9,5);
D=(0,5);
F=(3,0);
G=(6,0);
I=(4.5,5);
H=(3.5,1.67);
J=(5,3.33);
draw(A--B--C--D--cycle);
draw(A--C);
draw(F--I--G);
label("A",A,W);
label("B",B,E);
label("C",C,E);
label("D",D,W);
label("E",I,N);
label("F",F,S);
label("G",G,S);
label("H",H,NW);
label("J",J,NE);
[/asy]
Original LaTeX notation
In rectangle $ABCD$, points $F$ and $G$ lie on $\overline{AB}$ so that $AF = FG = GB$ and $E$ is the midpoint of $\overline{DC}$. Also, $\overline{AC}$ intersects $\overline{EF}$ at $H$ and $\overline{EG}$ at $J$. The area of rectangle $ABCD$ is 70. Find the area of triangle $EHJ$.

[asy]
pair A,B,C,D,I,F,G,H,J;
A=(0,0);
B=(9,0);
C=(9,5);
D=(0,5);
F=(3,0);
G=(6,0);
I=(4.5,5);
H=(3.5,1.67);
J=(5,3.33);
draw(A--B--C--D--cycle);
draw(A--C);
draw(F--I--G);
label("$A$",A,W);
label("$B$",B,E);
label("$C$",C,E);
label("$D$",D,W);
label("$E$",I,N);
label("$F$",F,S);
label("$G$",G,S);
label("$H$",H,NW);
label("$J$",J,NE);
[/asy]

level

Level 5

type

Geometry

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Source and history

task_id
b129a58d-b521-5f66-84d1-f78bcb66225f
task_key
geometry--test--b129a58d-b521-5f66-84d1-f78bcb66225f
task_revision_id
1
config / split
geometry / test

Official source

initial import