2005 AMC 12A Problems/Problem 7
Problem
Square is inside the square so that each side of can be extended to pass through a vertex of . Square has side length and . What is the area of the inner square ?
Solution
Arguable the hardest part of this question is to visualize the diagram. Since each side of can be extended to pass through a vertex of , we realize that must be tilted in such a fashion. Let a side of be .
Notice the right triangle (in blue) with legs and hypotenuse . By the Pythagorean Theorem, we have . Thus,
See also
2005 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 6 |
Followed by Problem 8 |
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All AMC 12 Problems and Solutions |