document.write( "Question 1158998: What is the radius of the largest circle that will fit inside a triangle that has two 15-inch
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Algebra.Com's Answer #781984 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "The given triangle is isosceles with congruent lateral sides of 15 inches long\r\n" );
document.write( "and the base of 18 inches.\r\n" );
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document.write( "The altitude of this triangle drawn to the 18-inches side, divide this triangle in two right-angled triangles.\r\n" );
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document.write( "This altitude is one leg of these triangles, while the other legs are 18/2 = 9 inches long.\r\n" );
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document.write( "From the Pythagorean theorem, the length of the altitude is   = 12 inches.\r\n" );
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document.write( "Then the area of the given triangle is   = 9*12 = 108 sq.inches.\r\n" );
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document.write( "Let the radius of the inscribed circle be r.\r\n" );
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document.write( "Now use the formula  \r\n" );
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document.write( "    area = \r\n" );
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document.write( "for the triangle, where P is the perimeter P of the triangle   P = 15+15+12 = 42 inches.\r\n" );
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document.write( "The area of the triangle is 108 sq.inches.\r\n" );
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document.write( "Hence,  108 = ,  which gives\r\n" );
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document.write( "    r =  =  =  =  inches.   ANSWER\r\n" );
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