Difference between revisions of "2011 AIME II Problems/Problem 2"
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== Problem 2 == | == Problem 2 == | ||
On [[square]] <math>ABCD</math>, point <math>E</math> lies on side <math>AD</math> and point <math>F</math> lies on side <math>BC</math>, so that <math>BE=EF=FD=30</math>. Find the area of the square <math>ABCD</math>. | On [[square]] <math>ABCD</math>, point <math>E</math> lies on side <math>AD</math> and point <math>F</math> lies on side <math>BC</math>, so that <math>BE=EF=FD=30</math>. Find the area of the square <math>ABCD</math>. |
Latest revision as of 16:02, 9 August 2018
Problem 2
On square , point lies on side and point lies on side , so that . Find the area of the square .
Solution
Drawing the square and examining the given lengths, you find that the three segments cut the square into three equal horizontal sections. Therefore, ( being the side length), , or . Solving for , we get , and
Area of the square is .
See also
2011 AIME II (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 | ||
All AIME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.