Difference between revisions of "2020 AMC 8 Problems/Problem 25"
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==Solution 2== | ==Solution 2== | ||
− | WLOG, assume that <math>S_1=S_3</math> and <math>R_1=R_2</math>. Let the sum of the lengths of <math>S_1</math> and <math>S_2</math> be <math>x</math> and let the length of <math>S_2</math> be <math>y</math>. We have the system < | + | WLOG, assume that <math>S_1=S_3</math> and <math>R_1=R_2</math>. Let the sum of the lengths of <math>S_1</math> and <math>S_2</math> be <math>x</math> and let the length of <math>S_2</math> be <math>y</math>. We have the system <cmath>x+y =3322</cmath> <cmath>x-y=2020</cmath> |
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which we solve to find that <math>y=\textbf{(A) }651</math>. | which we solve to find that <math>y=\textbf{(A) }651</math>. | ||
Revision as of 15:12, 18 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?
Solution 1
For each square , let the sidelength of this square be denoted by .
As the diagram shows, If we subtract the second equation from the first we will get or ~icematrix, edits by starrynight7210
Solution 2
WLOG, assume that and . Let the sum of the lengths of and be and let the length of be . We have the system
which we solve to find that .
-franzliszt
See also
2020 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 24 |
Followed by Last Problem | |
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 AJHSME/AMC 8 Problems and Solutions |
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