benchmarks.wiki

benchmarks.wiki / Public workspace

MATH / What is the value of x in the diagram?

Problem

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

problem

What is the value of xx in the diagram? [asy] import olympiad; draw((0,0)--(sqrt(3),0)--(0,sqrt(3))--cycle); draw((0,0)--(-3,0)--(0,sqrt(3))--cycle); label("232\sqrt{3}",(-3/2,sqrt(3)/2),NW); label("xx",(sqrt(3)/2,sqrt(3)/2),NE); draw("45∘45^{\circ}",(1.5,0),NW); draw("30∘30^{\circ}",(-2.45,0),NE); draw(rightanglemark((0,sqrt(3)),(0,0),(sqrt(3),0),5)); [/asy]
Plain-text mathematical notation (without MathML)
What is the value of x in the diagram?

[asy]

import olympiad;

draw((0,0)--(sqrt(3),0)--(0,sqrt(3))--cycle);

draw((0,0)--(-3,0)--(0,sqrt(3))--cycle);

label("2√(3)",(-3/2,sqrt(3)/2),NW);

label("x",(sqrt(3)/2,sqrt(3)/2),NE);

draw("45^(∘)",(1.5,0),NW);

draw("30^(∘)",(-2.45,0),NE);

draw(rightanglemark((0,sqrt(3)),(0,0),(sqrt(3),0),5));

[/asy]
Original LaTeX notation
What is the value of $x$ in the diagram?

[asy]

import olympiad;

draw((0,0)--(sqrt(3),0)--(0,sqrt(3))--cycle);

draw((0,0)--(-3,0)--(0,sqrt(3))--cycle);

label("$2\sqrt{3}$",(-3/2,sqrt(3)/2),NW);

label("$x$",(sqrt(3)/2,sqrt(3)/2),NE);

draw("$45^{\circ}$",(1.5,0),NW);

draw("$30^{\circ}$",(-2.45,0),NE);

draw(rightanglemark((0,sqrt(3)),(0,0),(sqrt(3),0),5));

[/asy]

level

Level 5

type

Prealgebra

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
a5111985-492c-5c54-b364-093668c8dc93
task_key
prealgebra--test--a5111985-492c-5c54-b364-093668c8dc93
task_revision_id
1
config / split
prealgebra / test

Official source

initial import