benchmarks.wiki

benchmarks.wiki / Public workspace

MATH / In the figure below, side AE of rectangle ABDE is parallel to the x-axis, and side BD contains the point C. The vertices of triangle ACE are A(1,1), C(3,3) and E(4,1). What is the …

Problem

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

problem

In the figure below, side AEAE of rectangle ABDEABDE is parallel to the xx-axis, and side BDBD contains the point CC. The vertices of triangle ACEACE are A(1,1)A(1, 1), C(3,3)C(3, 3) and E(4,1)E(4, 1). What is the ratio of the area of triangle ACEACE to the area of rectangle ABDEABDE? Express your answer as a common fraction. [asy]unitsize(1inch); draw((0,0)--(4.5,0),Arrow); draw((0,0)--(0,3.5),Arrow); draw((-0.1,1)--(0.1,1)); draw((-0.1,2)--(0.1,2)); draw((-0.1,3)--(0.1,3)); draw((1,0.1)--(1,-0.1)); draw((2,0.1)--(2,-0.1)); draw((3,0.1)--(3,-0.1)); draw((4,0.1)--(4,-0.1)); draw((1,1)--(1,3)--(4,3)--(4,1)--cycle); draw((1,1)--(3,3)--(4,1)); fill((1,1)--(3,3)--(1,3)--cycle,gray(0.7)); fill((3,3)--(4,3)--(4,1)--cycle,gray(0.7)); label("AA",(1,1),SW); label("BB",(1,3),NW); label("CC",(3,3),N); label("DD",(4,3),NE); label("EE",(4,1),SE); [/asy]
Plain-text mathematical notation (without MathML)
In the figure below, side AE of rectangle ABDE is parallel to the x-axis, and side BD contains the point C. The vertices of triangle ACE are A(1,1), C(3,3) and E(4,1). What is the ratio of the area of triangle ACE to the area of rectangle ABDE? Express your answer as a common fraction.

[asy]unitsize(1inch);
draw((0,0)--(4.5,0),Arrow);
draw((0,0)--(0,3.5),Arrow);
draw((-0.1,1)--(0.1,1));
draw((-0.1,2)--(0.1,2));
draw((-0.1,3)--(0.1,3));
draw((1,0.1)--(1,-0.1));
draw((2,0.1)--(2,-0.1));
draw((3,0.1)--(3,-0.1));
draw((4,0.1)--(4,-0.1));
draw((1,1)--(1,3)--(4,3)--(4,1)--cycle);
draw((1,1)--(3,3)--(4,1));
fill((1,1)--(3,3)--(1,3)--cycle,gray(0.7));
fill((3,3)--(4,3)--(4,1)--cycle,gray(0.7));
label("A",(1,1),SW);
label("B",(1,3),NW);
label("C",(3,3),N);
label("D",(4,3),NE);
label("E",(4,1),SE);
[/asy]
Original LaTeX notation
In the figure below, side $AE$ of rectangle $ABDE$ is parallel to the $x$-axis, and side $BD$ contains the point $C$. The vertices of triangle $ACE$ are $A(1, 1)$, $C(3, 3)$ and $E(4, 1)$. What is the ratio of the area of triangle $ACE$ to the area of rectangle $ABDE$? Express your answer as a common fraction.

[asy]unitsize(1inch);
draw((0,0)--(4.5,0),Arrow);
draw((0,0)--(0,3.5),Arrow);
draw((-0.1,1)--(0.1,1));
draw((-0.1,2)--(0.1,2));
draw((-0.1,3)--(0.1,3));
draw((1,0.1)--(1,-0.1));
draw((2,0.1)--(2,-0.1));
draw((3,0.1)--(3,-0.1));
draw((4,0.1)--(4,-0.1));
draw((1,1)--(1,3)--(4,3)--(4,1)--cycle);
draw((1,1)--(3,3)--(4,1));
fill((1,1)--(3,3)--(1,3)--cycle,gray(0.7));
fill((3,3)--(4,3)--(4,1)--cycle,gray(0.7));
label("$A$",(1,1),SW);
label("$B$",(1,3),NW);
label("$C$",(3,3),N);
label("$D$",(4,3),NE);
label("$E$",(4,1),SE);
[/asy]

level

Level 2

type

Geometry

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
762ca880-9b4f-5f53-bc65-52291bf57ff6
task_key
geometry--test--762ca880-9b4f-5f53-bc65-52291bf57ff6
task_revision_id
1
config / split
geometry / test

Official source

initial import