Difference between revisions of "2006 AMC 10B Problems/Problem 15"
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== See Also == | == See Also == | ||
*[[2006 AMC 10B Problems]] | *[[2006 AMC 10B Problems]] | ||
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Revision as of 15:01, 2 August 2006
Problem
Rhombus is similar to rhombus
. The area of rhombus
is
and
. What is the area of rhombus
?
Solution
Using properties of a rhombus:
.
.
It is easy to see that rhombus is made up of equilateral triangles
and
.
Let the lengths of the sides of rhombus be
.
The longer diagonal of rhombus is
. Since
is a side of an equilateral triangle with a side length of
,
.
The longer diagonal of rhombus is
. Since
is twice the length of an altitude of of an equilateral triangle with a side length of
,
The ratio of the longer diagonal of rhombus to rhombus
is
Therefore, the ratio of the area of rhombus to rhombus
is
Let be the area of rhombus
.