MathDB
Arithmetic Progression in Quadrilateral

Source: 2021 AMC 12A (Fall) #24

November 11, 2021
arithmetic sequence

Problem Statement

Convex quadrilateral ABCDABCD has AB = 18, \angle{A} = 60 \textdegree, and ABCD\overline{AB} \parallel \overline{CD}. In some order, the lengths of the four sides form an arithmetic progression, and side AB\overline{AB} is a side of maximum length. The length of another side is aa. What is the sum of all possible values of aa?
<spanclass=latexbold>(A)</span>24<spanclass=latexbold>(B)</span>42<spanclass=latexbold>(C)</span>60<spanclass=latexbold>(D)</span>66<spanclass=latexbold>(E)</span>84<span class='latex-bold'>(A) </span> 24 \qquad <span class='latex-bold'>(B) </span> 42 \qquad <span class='latex-bold'>(C) </span> 60 \qquad <span class='latex-bold'>(D) </span> 66 \qquad <span class='latex-bold'>(E) </span> 84