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MATH / Squares ABCD and EFGH are equal in area. Vertices B, E, C, and H lie on the same line. Diagonal AC is extended to J, the midpoint of GH. What is the fraction of the two squares tha…

Problem

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

problem

Squares ABCDABCD and EFGHEFGH are equal in area. Vertices BB, EE, CC, and HH lie on the same line. Diagonal ACAC is extended to JJ, the midpoint of GHGH. What is the fraction of the two squares that is shaded? [asy] fill((0,4)--(4,4)--(4,0)--cycle,gray); fill((4,0)--(6,0)--(6,-2)--cycle,gray); draw((0,0)--(4,0)--(4,4)--(0,4)--cycle,linewidth(1)); draw((2,0)--(6,0)--(6,-4)--(2,-4)--cycle,linewidth(1)); draw((0,4)--(6,-2),linewidth(1)); label("AA",(0,4),NW); label("BB",(0,0),W); label("CC",(4,0),NE); label("DD",(4,4),NE); label("EE",(2,0),SW); label("FF",(2,-4),SW); label("GG",(6,-4),SE); label("HH",(6,0),E); label("JJ",(6,-2),E); [/asy]
Plain-text mathematical notation (without MathML)
Squares ABCD and EFGH are equal in area.  Vertices B, E, C, and H lie on the same line.  Diagonal AC is extended to J, the midpoint of GH.  What is the fraction of the two squares that is shaded? [asy]
fill((0,4)--(4,4)--(4,0)--cycle,gray);
fill((4,0)--(6,0)--(6,-2)--cycle,gray);
draw((0,0)--(4,0)--(4,4)--(0,4)--cycle,linewidth(1));
draw((2,0)--(6,0)--(6,-4)--(2,-4)--cycle,linewidth(1));
draw((0,4)--(6,-2),linewidth(1));
label("A",(0,4),NW);
label("B",(0,0),W);
label("C",(4,0),NE);
label("D",(4,4),NE);
label("E",(2,0),SW);
label("F",(2,-4),SW);
label("G",(6,-4),SE);
label("H",(6,0),E);
label("J",(6,-2),E);
[/asy]
Original LaTeX notation
Squares $ABCD$ and $EFGH$ are equal in area.  Vertices $B$, $E$, $C$, and $H$ lie on the same line.  Diagonal $AC$ is extended to $J$, the midpoint of $GH$.  What is the fraction of the two squares that is shaded? [asy]
fill((0,4)--(4,4)--(4,0)--cycle,gray);
fill((4,0)--(6,0)--(6,-2)--cycle,gray);
draw((0,0)--(4,0)--(4,4)--(0,4)--cycle,linewidth(1));
draw((2,0)--(6,0)--(6,-4)--(2,-4)--cycle,linewidth(1));
draw((0,4)--(6,-2),linewidth(1));
label("$A$",(0,4),NW);
label("$B$",(0,0),W);
label("$C$",(4,0),NE);
label("$D$",(4,4),NE);
label("$E$",(2,0),SW);
label("$F$",(2,-4),SW);
label("$G$",(6,-4),SE);
label("$H$",(6,0),E);
label("$J$",(6,-2),E);
[/asy]

level

Level 4

type

Geometry

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Source and history

task_id
412c2155-e1f6-540f-bce8-c26c002f4d56
task_key
geometry--test--412c2155-e1f6-540f-bce8-c26c002f4d56
task_revision_id
1
config / split
geometry / test

Official source

initial import