Difference between revisions of "2020 AMC 12A Problems/Problem 2"
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The acronym AMC is shown in the rectangular grid below with grid lines spaced <math>1</math> unit apart. In units, what is the sum of the lengths of the line segments that form the acronym AMC<math>?</math> | The acronym AMC is shown in the rectangular grid below with grid lines spaced <math>1</math> unit apart. In units, what is the sum of the lengths of the line segments that form the acronym AMC<math>?</math> | ||
| − | + | <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), dashed); | ||
| + | } | ||
| + | if (i != 2) { | ||
| + | draw((j,i)--(j,i+1), 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> | ||
| + | |||
<math>\textbf{(A) } 17 \qquad \textbf{(B) } 15 + 2\sqrt{2} \qquad \textbf{(C) } 13 + 4\sqrt{2} \qquad \textbf{(D) } 11 + 6\sqrt{2} \qquad \textbf{(E) } 21</math> | <math>\textbf{(A) } 17 \qquad \textbf{(B) } 15 + 2\sqrt{2} \qquad \textbf{(C) } 13 + 4\sqrt{2} \qquad \textbf{(D) } 11 + 6\sqrt{2} \qquad \textbf{(E) } 21</math> | ||
Revision as of 08:00, 1 February 2020
Problem
The acronym AMC is shown in the rectangular grid below with grid lines spaced 
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), dashed); } if (i != 2) { draw((j,i)--(j,i+1), 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]](http://latex.artofproblemsolving.com/6/6/4/6649eb6b62018218d4086bde7597f2da9b4b10e3.png)
See Also
| 2020 AMC 12A (Problems • Answer Key • Resources) | |
| Preceded by Problem 1 |
Followed by Problem 3 |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | |
| All AMC 12 Problems and Solutions | |
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. 
