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AMC (AIMO validation set) / https://artofproblemsolving.com/wiki/index.php/2023_AMC_12B_Problems/Problem_17 / Triangle ABC has side lengths in arithmetic progression, and the smallest side has length 6. If the triangle has an angle of 120^(∘), Find the area of ABC. The final answer can be …

Problem

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

problem

Triangle

ABC

has side lengths in arithmetic progression, and the smallest side has length

6.

If the triangle has an angle of

120^\circ,

Find the area of

ABC

. The final answer can be simplified in the form

m \sqrt{n}

, where

m

and

n

are positive integers and

n

without square factore. What is

m+n

Plain-text mathematical notation (without MathML)

Triangle ABC has side lengths in arithmetic progression, and the smallest side has length 6. If the triangle has an angle of 120^(∘), Find the area of ABC. The final answer can be simplified in the form m√(n), where m and n are positive integers and n without square factore. What is m+n?

Original LaTeX notation

Triangle $ABC$ has side lengths in arithmetic progression, and the smallest side has length $6.$ If the triangle has an angle of $120^\circ,$ Find the area of $ABC$. The final answer can be simplified in the form $m \sqrt{n}$, where $m$ and $n$ are positive integers and $n$ without square factore. What is $m+n$?

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Source and history

upstream_id / Original problem ID: https://artofproblemsolving.com/wiki/index.php/2023_AMC_12B_Problems/Problem_17
task_id: 6f7ee6ba-f7a1-5877-a903-3d5e181528ec
task_key: default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2023~5fAMC~5f12B~5fProblems~2fProblem~5f17
task_revision_id: 2
config / split: default / train

Official source

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