document.write( "Question 1085018: I need to solve this problem please its on this link \r
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Algebra.Com's Answer #699154 by ikleyn(52847) $\"\"$ $\"About$

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\n" ); document.write( "The area of the rhombus is    $\"A%5Brhombus%5D\"$ = $\"4%2A%28%28ab%29%2F2%29\"$ = 2ab   (four congruent right-angled triangles).\r
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\n" ); document.write( "\n" ); document.write( "The side length of the rhombus is   L = $\"sqrt%28a%5E2%2Bb%5E2%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "The perimeter of the rhombus is   4L = $\"4%2Asqrt%28a%5E2+%2B+b%5E2%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "The semi-perimeter of the rhombus is   s = $\"%284L%29%2F2\"$ = $\"2%2Asqrt%28a%5E2+%2B+b%5E2%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "The radius of the inscribed circle into the rhombus is   r = $\"A%5Brhombus%5D%2Fs\"$ = $\"%282ab%29%2F%282%2Asqrt%28a%5E2%2B+b%5E2%29%29\"$ = $\"%28ab%29%2Fsqrt%28a%5E2%2Bb%5E2%29\"$ . \r
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document.write( "     Regarding the formula  r =   for the radius of inscribed circle into convex polygon, where A is the area of the polygon \r\n" );
document.write( "     and s is its semi-perimeter, see the lesson \r\n" );
document.write( "         Area of n-sided polygon circumscribed about a circle\r\n" );
document.write( "     in this site.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Thus the area of the inscribed circle into the rhombus is $\"A%5Bcircle%5D\"$ = $\"pi%2A%28%28a%5E2%2Ab%5E2%29%2F%28a%5E2+%2B+b%5E2%29%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Finally, the ratio $\"A%5Bcircle%5D%2FA%5Brhombus%5D\"$ , which is under the question, is\r
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\n" ); document.write( "\n" ); document.write( " $\"A%5Bcircle%5D%2FA%5Brhombus%5D\"$ = $\"%28pi%2A%28%28a%5E2%2Ab%5E2%29%2F%28a%5E2+%2B+b%5E2%29%29%29%2F%282ab%29\"$ = $\"%28pi%2Aa%2Ab%29%2F%282%2A%28a%5E2%2Bb%5E2%29%29\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "Also, you have this free of charge online textbook on Geometry\r
\n" ); document.write( "\n" ); document.write( " GEOMETRY - YOUR ONLINE TEXTBOOK \r
\n" ); document.write( "\n" ); document.write( "in this site.\r
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\n" ); document.write( "\n" ); document.write( "The referred lesson is the part of this online textbook under the topic \"Area of polygons\".\r
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