2008 AMC 10A Problems/Problem 10
Contents
Problem
Each of the sides of a square with area is bisected, and a smaller square is constructed using the bisection points as vertices. The same process is carried out on to construct an even smaller square . What is the area of ?
Solution 1
Since the area of the large square is , the side length equals . If all sides are bisected, the resulting square has side length , thus making the area . If we repeat this process again, we notice that the area is just half that of the previous square, so the area of
Solution 2
Since the length ratio is , then the area ratio is (since the area ratio between two similar 2-dimensional objects is equal to the side ratio of those objects squared). This means that and .
See also
2008 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 9 |
Followed by Problem 11 | |
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All AMC 10 Problems and Solutions |
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