2007 AMC 12A Problems/Problem 23
Problem
Square has area
and
is parallel to the x-axis. Vertices
, and
are on the graphs of
and
respectively. What is
Solution
Let be the x-coordinate of
and
, and
be the x-coordinate of
and
be the y-coordinate of
and
. Then
and
. Since the distance between
and
is
, we have
, yielding
.
However, we can discard the negative root (all three logarithmic equations are underneath the line and above
when
is negative, hence we can't squeeze in a square of side 6). Thus
.
Substituting back, , so
.
See also
2007 AMC 12A (Problems • Answer Key • Resources) | |
Preceded by Problem 22 |
Followed by Problem 24 |
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All AMC 12 Problems and Solutions |