2020 AMC 12A Problems/Problem 2: Difference between revisions
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~IceMatrix | ~IceMatrix | ||
==Video Solution== | |||
https://youtu.be/vtCOv0kxuNE | |||
~Education, the Study of Everything | |||
==See Also== | ==See Also== | ||
Revision as of 03:18, 7 October 2022
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)
Solution 1
Each of the straight line segments have length and each of the slanted line segments have length 
(this can be deducted using 
, pythag, trig, or just sense)
There area a total of 
straight lines segments and 
slanted line segments. The sum is 
~quacker88
Solution 2
Either count the straight or diagonals and deduce from the answers that the only answer possible is .
Solution 3
There are 4 slanted segments. Therefore, the only answer would be .
Video Solution
~IceMatrix
Video Solution
~Education, the Study of Everything
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. 
