document.write( "Question 620349: http://img.geocaching.com/cache/large/8f671ade-1846-4e62-b2d7-2c73512ae1c8.gif\r
\n" ); document.write( "\n" ); document.write( "Three big one-inch squares (S3) are joined corner-to-corner to make an equilateral triangle. Inside that triangle, three little squares (S1) are fit into a similar shape. Finally, the line segment from the little square to the corner of the large triangle is used to form the medium square (S2) as shown.
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\n" ); document.write( "What is the ratio of areas of the medium square to the little square (S2:S1)? \n" ); document.write( "

Algebra.Com's Answer #390101 by KMST(5328) $\"\"$ $\"About$

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I see three little kites in the corners of the triangle.
\n" ); document.write( "If you split one of them along the long diagonal, you get two congruent 30-60-90 right triangles.
\n" ); document.write( "The ratio of short leg to long leg in those triangles (and in all 30-60-90 right triangles) is $\"1%2Fsqrt%283%29\"$ .
\n" ); document.write( "(It is usually written as $\"tan%2830%5Eo%29=sqrt%283%29%2F3\"$ just for elegance, but it works better for me as $\"1%2Fsqrt%283%29\"$ in this case).
\n" ); document.write( "That is the ratio of the side of the small square to the side of the medium square.
\n" ); document.write( "The ratio of their areas is the square of the ratio of their sides, or $\"highlight%281%2F3%29\"$ . \n" ); document.write( "

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