document.write( "Question 1206000: the altitude to the hypotenuse of a right triangle divides the hypotenuse in the ratio 4:1. what is the ratio of legs of the triangle?
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Algebra.Com's Answer #843156 by ikleyn(52776) $\"\"$ $\"About$

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document.write( "Let x and y be the segments the altitude divides the hypotenuse.\r\n" );
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document.write( "Then the altitude drawn to the hypotenuse is  the mean geometric value of x and y,  h = .   \r\n" );
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document.write( "    +---------------------------------------------------------------------+\r\n" );
document.write( "    |    This remarkable formula is from the basic course of Geometry.    |\r\n" );
document.write( "    |                  It is your pre-requisite.                          |\r\n" );
document.write( "    |   It is assumed you know it from your previous course of Geometry.  |\r\n" );
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document.write( "We are given that y = 4x;  so,  h =  =  = 2x.\r\n" );
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document.write( "Thus the ratio    is   = 2.\r\n" );
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document.write( "           |      In other words, the ratio of the legs       |\r\n" );
document.write( "           |    of the smallest right-angled triangle is 2.   |\r\n" );
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document.write( "The smallest triangle of the division is SIMILAR to the original large triangle,\r\n" );
document.write( "since they both are right-angled triangles and have one common acute angle.\r\n" );
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document.write( "So, in the original right-angled triangle, the ratio of the longer leg to the shorter leg is 2, too.\r\n" );
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document.write( "ANSWER.  In the original triangle, the ratio of the longer leg to the shorter leg is 2.\r\n" );
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