Difference between revisions of "2006 AMC 10B Problems/Problem 15"
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== See Also == | == See Also == | ||
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+ | *[[2006 AMC 10B Problems/Problem 16|Next Problem]] |
Revision as of 14:01, 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 .