document.write( "Question 1198962: Lines drawn parallel to the base of the triangle pictured, separate the other two sides into 10 equally spaced parts. What percentage of the triangle is grey? \n" ); document.write( "

Algebra.Com's Answer #832653 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "The area of the k-th triangle is    of the area of the greatest triangle, A.\r\n" );
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document.write( "Therefore, the area of k-th individual single shape is  \r\n" );
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document.write( "     -   of the area of greatest triangle, A,    (1)\r\n" );
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document.write( "or\r\n" );
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document.write( "     =  = .    (2)\r\n" );
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document.write( "From here, the area of the grey part is\r\n" );
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document.write( "    A(grey) =  = .      (3)\r\n" );
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document.write( "(summing all (2k-1) over k = 1, 3, 5, 7, 9)\r\n" );
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document.write( "The area of the unshaded (white) part is\r\n" );
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document.write( "    A(white) =  = .    (4)\r\n" );
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document.write( "(summing all (2k-1) over k = 2, 4, 6, 8, 10)\r\n" );
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document.write( "Therefore,  the ratio under the problem's question is\r\n" );
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document.write( "     =  = .    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "Surely, one can avoid calculating unshaded area (4), when the area of grey part (3) is just calculated.\r
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\n" ); document.write( "\n" ); document.write( "I did it only for the purpose of completeness.\r
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