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Source: 2023 AMC 12B #17

November 15, 2023
AMCAMC 12geometryarithmetic sequence2023 AMC2023 AMC 12B

Problem Statement

Triangle ABCABC has side lengths in arithmetic progression, and the smallest side has length 6.6. If the triangle has an angle of 120∘,120^\circ, what is the area of ABCABC?
<spanclass=′latex−bold′>(A)</span> 123<spanclass=′latex−bold′>(B)</span> 86<spanclass=′latex−bold′>(C)</span> 142<spanclass=′latex−bold′>(D)</span> 202<spanclass=′latex−bold′>(E)</span> 153<span class='latex-bold'>(A)</span>\ 12\sqrt 3 \qquad<span class='latex-bold'>(B)</span>\ 8\sqrt 6 \qquad<span class='latex-bold'>(C)</span>\ 14\sqrt 2 \qquad<span class='latex-bold'>(D)</span>\ 20\sqrt 2 \qquad<span class='latex-bold'>(E)</span>\ 15\sqrt 3
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