Difference between revisions of "2022 AMC 12A Problems/Problem 3"
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Notice how the only dimension not used in the list was <math>2\times 4</math> and that corresponds with B so the answer is, <math>\textbf{(B) }B.</math> | Notice how the only dimension not used in the list was <math>2\times 4</math> and that corresponds with B so the answer is, <math>\textbf{(B) }B.</math> | ||
| − | ~ghfhgvghj10 | + | ~ghfhgvghj10 & Education, the study of everything. |
Revision as of 15:56, 19 November 2022
Solution 1 (List)
![[asy] fill((3,2.5)--(3,4.5)--(5.3,4.5)--(5.3,2.5)--cycle,mediumgray); draw((0,0)--(7,0)--(7,7)--(0,7)--(0,0)); draw((3,0)--(3,4.5)); draw((0,4.5)--(5.3,4.5)); draw((5.3,7)--(5.3,2.5)); draw((7,2.5)--(3,2.5)); label("A",(0,0),S); label("B",(3,0),S); label("C",(7,0),S); label("D",(7.5,3),S); label("E",(7.5,7.8),S); label("F",(5.5,7.8),S); label("G",(-.5,7.8),S); label("H",(-.5,5),S); [/asy]](http://latex.artofproblemsolving.com/1/a/9/1a9c62fa198edf2a60c39f5ba36baeded1154343.png)
By finding the dimensions of the middle rectangle, we need to find the dimensions of the other 4 rectangles. By doing this, there is going to be a rule.
Rule: 
Let's make a list of all the dimensions of the rectangles from the diagram. We have to fill in the dimensions from up above, but still apply to the rule.
By applying the rule, we get 
, and 
By substitution, we get this list
Notice how the only dimension not used in the list was 
and that corresponds with B so the answer is, 
~ghfhgvghj10 & Education, the study of everything.
