MathDB
AMC Acronym

Source: 2020 AMC 12A #2

January 31, 2020
AMCAMC 12AMC 12 A2020 AMC 12A2020 AMC

Problem Statement

The acronym AMC is shown in the rectangular grid below with grid lines spaced 11 unit apart. In units, what is the sum of the lengths of the line segments that form the acronym AMC??
[asy] import olympiad; unitsize(25); for (int i = 0; i < 3; ++i) { for (int j = 0; j < 9; ++j) { pair A = (j,i);
} } for (int i = 0; i < 3; ++i) { for (int j = 0; j < 9; ++j) { if (j != 8) { draw((j,i)--(j+1,i), gray(0.6)+dashed); } if (i != 2) { draw((j,i)--(j,i+1), gray(0.6)+dashed); } } } draw((0,0)--(2,2),linewidth(2)); draw((2,0)--(2,2),linewidth(2)); draw((1,1)--(2,1),linewidth(2)); draw((3,0)--(3,2),linewidth(2)); draw((5,0)--(5,2),linewidth(2)); draw((4,1)--(3,2),linewidth(2)); draw((4,1)--(5,2),linewidth(2)); draw((6,0)--(8,0),linewidth(2)); draw((6,2)--(8,2),linewidth(2)); draw((6,0)--(6,2),linewidth(2)); [/asy]
<spanclass=latexbold>(A)</span>17<spanclass=latexbold>(B)</span>15+22<spanclass=latexbold>(C)</span>13+42<spanclass=latexbold>(D)</span>11+62<spanclass=latexbold>(E)</span>21<span class='latex-bold'>(A) </span> 17 \qquad <span class='latex-bold'>(B) </span> 15 + 2\sqrt{2} \qquad <span class='latex-bold'>(C) </span> 13 + 4\sqrt{2} \qquad <span class='latex-bold'>(D) </span> 11 + 6\sqrt{2} \qquad <span class='latex-bold'>(E) </span> 21