benchmarks.wiki

benchmarks.wiki / Public workspace

MATH / Several figures can be made by attaching two equilateral triangles to the…

Problem

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

problem

Several figures can be made by attaching two equilateral triangles to the regular pentagon ABCDEABCDE in two of the five positions shown. How many non-congruent figures can be constructed in this way? [asy] pair A,B,C,D,I; A=(10,0); B=(0,0); C=(-3.1,9.5); D=(5,15.4); I=(13.1,9.5); draw(A--B--C--D--I--cycle,linewidth(0.7)); draw(A--B--(5,-8.7)--cycle,dashed); draw(A--I--(19.8,2.1)--cycle,dashed); draw(C--B--(-9.8,2.1)--cycle,dashed); draw(I--D--(14.15,19.4)--cycle,dashed); draw(D--C--(-4.15,19.4)--cycle,dashed); label("AA",A,SE); label("BB",B,SW); label("CC",C,W); label("EE",I,E); label("DD",D,N); [/asy]
Plain-text mathematical notation (without MathML)
Several figures can be made by attaching two equilateral triangles to the regular pentagon ABCDE in two of the five positions shown. How many non-congruent figures can be constructed in this way?

[asy]
pair A,B,C,D,I;
A=(10,0);
B=(0,0);
C=(-3.1,9.5);
D=(5,15.4);
I=(13.1,9.5);
draw(A--B--C--D--I--cycle,linewidth(0.7));
draw(A--B--(5,-8.7)--cycle,dashed);
draw(A--I--(19.8,2.1)--cycle,dashed);
draw(C--B--(-9.8,2.1)--cycle,dashed);
draw(I--D--(14.15,19.4)--cycle,dashed);
draw(D--C--(-4.15,19.4)--cycle,dashed);
label("A",A,SE);
label("B",B,SW);
label("C",C,W);
label("E",I,E);
label("D",D,N);
[/asy]
Original LaTeX notation
Several figures can be made by attaching two equilateral triangles to the regular pentagon $ABCDE$ in two of the five positions shown. How many non-congruent figures can be constructed in this way?

[asy]
pair A,B,C,D,I;
A=(10,0);
B=(0,0);
C=(-3.1,9.5);
D=(5,15.4);
I=(13.1,9.5);
draw(A--B--C--D--I--cycle,linewidth(0.7));
draw(A--B--(5,-8.7)--cycle,dashed);
draw(A--I--(19.8,2.1)--cycle,dashed);
draw(C--B--(-9.8,2.1)--cycle,dashed);
draw(I--D--(14.15,19.4)--cycle,dashed);
draw(D--C--(-4.15,19.4)--cycle,dashed);
label("$A$",A,SE);
label("$B$",B,SW);
label("$C$",C,W);
label("$E$",I,E);
label("$D$",D,N);
[/asy]

level

Level 4

type

Counting & Probability

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
e244934c-5c25-5245-b85a-4bb8d07590c9
task_key
counting~5fand~5fprobability--test--e244934c-5c25-5245-b85a-4bb8d07590c9
task_revision_id
1
config / split
counting_and_probability / test

Official source

initial import