Algebra.Com's Answer #847666 by ikleyn(52873)![\"\"](\"/images/stars/stars-13.gif\")  
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document.write( "There are two equilateral triangles with different areas, where O and O' are t
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document.write( "heir circumcenters respectively. In the first, the distance OA is 9 cm,
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document.write( "and in the second, the distance O'C' is 4√2 cm.
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document.write( "Find the ratio of the area of the first to the area of the second.
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document.write( "https://ibb.co/Cz6tWsL
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document.write( "These equilateral triangles are similar (as any two equilateral triangles,\r\n" );
document.write( "by three angles). \r\n" );
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document.write( "Their corresponding similar elements are OC and O'C'.\r\n" );
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document.write( "In the second triangle, we are given O'C' =  cm.\r\n" );
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document.write( "In the first triangle, we are given OA = 9 cm.\r\n" );
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document.write( " But triangle OAC is a right-angled 90°-60°-30°-triangle;\r\n" );
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document.write( " therefore, the hypotenuse OC is twice the leg OA,\r\n" );
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document.write( " so, the hypotenuse OC is 2*9 = 18 cm.\r\n" );
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document.write( "Thus, the ratio of corresponding linear dimensions in triangles is\r\n" );
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document.write( " OC 18 9 9*sqrt(2)\r\n" );
document.write( " ----- = ----------- = -------- = ----------.\r\n" );
document.write( " O'C' 4*sqrt(2) 2*sqrt(2) 4\r\n" );
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document.write( "The ratio of the areas of the second triangle to the first triangle is the square\r\n" );
document.write( "of the ratio of their corresponding linear elements, i.e.\r\n" );
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document.write( "  =  =  = 10.125. ANSWER\r\n" );
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document.write( "Solved.\r
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