document.write( "Question 1143115: Three sides of a triangle measures 12 cm, 18 cm and 10 cm. Find the altitude of the longest side, the median of the longest side, the length of angle bisector of the largest angle and the line segment joining the midpoints of 12 cm and 18 cm sides. Thanks.
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Algebra.Com's Answer #763883 by ikleyn(52797) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "(a)  To find the area of the triangle, use the Heron's formula.\r\n" );
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document.write( "         On the Heron's formula, see the lessons\r\n" );
document.write( "             Proof of the Heron's formula for the area of a triangle \r\n" );
document.write( "             One more proof of the Heron's formula for the area of a triangle \r\n" );
document.write( "         in this site.\r\n" );
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document.write( "     The semi-perimeter is equal to s =  = 20 cm.\r\n" );
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document.write( "     The area of the triangle is (Heron's formula)\r\n" );
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document.write( "         A =  =  =  =  = 56.57  cm^2  (approximately).    ANSWER\r\n" );
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document.write( "(b)  Altitude to the longest side.\r\n" );
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document.write( "     Let h be the altitude to the longest side.\r\n" );
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document.write( "     Then for the area of the triangle,\r\n" );
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document.write( "         A =  = 56.57  cm^2,\r\n" );
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document.write( "     which implies \r\n" );
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document.write( "         h =  = 6.29 cm  (approximately).     ANSWER\r\n" );
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document.write( "(c)  The median to the longest side.\r\n" );
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document.write( "     In a triangle with the sides \"a\", \"b\" and \"c\", the median drawn to the side \"c\" has the length of \r\n" );
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document.write( "          = .\r\n" );
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document.write( "        For this theorem, see the lesson\r\n" );
document.write( "            The length of a median of a triangle\r\n" );
document.write( "        in this site.\r\n" );
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document.write( "      Substitute the given data  a= 12, b= 10, c= 18 to get the length of the median drawn to the side of the length 18 cm\r\n" );
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document.write( "          =  =  = 6.403 cm.      ANSWER\r\n" );
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document.write( "d.  The length of angle bisector of the largest angle of the triangle.\r\n" );
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document.write( "    If the triangle is not isosceles, then this problem (this question) is FAR BEYOND any school Math curriculum.\r\n" );
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document.write( "e.   The line segment joining the midpoints of 12 cm and 18 cm sides\r\n" );
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document.write( "     It is called \"the mid-segment\" of the triangle.\r\n" );
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document.write( "     It is widely known that the mid-segment length is half of the length of the parallel side of the triangle.\r\n" );
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document.write( "      So, the answer is   = 5 cm in this case.\r\n" );
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document.write( "    Do not include so many questions in your posts.\r\n" );
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