Difference between revisions of "2020 AMC 8 Problems/Problem 25"
(Created page with "<math>25.</math> Rectangles <math>R_1</math> and <math>R_2,</math> and squares <math>S_1,\,S_2,\,</math> and <math>S_3,</math> shown below, combine to form a rectangle that is...") |
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| − | + | Rectangles <math>R_1</math> and <math>R_2,</math> and squares <math>S_1,\,S_2,\,</math> and <math>S_3,</math> shown below, combine to form a rectangle that is 3322 units wide and 2020 units high. What is the side length of <math>S_2</math> in units? | |
| − | + | <asy> | |
draw((0,0)--(5,0)--(5,3)--(0,3)--(0,0)); | draw((0,0)--(5,0)--(5,3)--(0,3)--(0,0)); | ||
draw((3,0)--(3,1)--(0,1)); | draw((3,0)--(3,1)--(0,1)); | ||
draw((3,1)--(3,2)--(5,2)); | draw((3,1)--(3,2)--(5,2)); | ||
draw((3,2)--(2,2)--(2,1)--(2,3)); | draw((3,2)--(2,2)--(2,1)--(2,3)); | ||
| − | label(" | + | label("$R_1$",(3/2,1/2)); |
| − | label(" | + | label("$S_3$",(4,1)); |
| − | label(" | + | label("$S_2$",(5/2,3/2)); |
| − | label(" | + | label("$S_1$",(1,2)); |
| − | label(" | + | label("$R_2$",(7/2,5/2)); |
| − | + | </asy> | |
<math>\textbf{(A) }651 \qquad \textbf{(B) }655 \qquad \textbf{(C) }656 \qquad \textbf{(D) }662 \qquad \textbf{(E) }666</math> | <math>\textbf{(A) }651 \qquad \textbf{(B) }655 \qquad \textbf{(C) }656 \qquad \textbf{(D) }662 \qquad \textbf{(E) }666</math> | ||
Revision as of 22:14, 17 November 2020
Rectangles 
and 
and squares 
and 
shown below, combine to form a rectangle that is 3322 units wide and 2020 units high. What is the side length of 
in units?
![[asy] draw((0,0)--(5,0)--(5,3)--(0,3)--(0,0)); draw((3,0)--(3,1)--(0,1)); draw((3,1)--(3,2)--(5,2)); draw((3,2)--(2,2)--(2,1)--(2,3)); label("$R_1$",(3/2,1/2)); label("$S_3$",(4,1)); label("$S_2$",(5/2,3/2)); label("$S_1$",(1,2)); label("$R_2$",(7/2,5/2)); [/asy]](http://latex.artofproblemsolving.com/a/5/5/a55c518a1179d67520c6a03827b4ba25ca1413f2.png)
