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, you get a square of 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 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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