document.write( "Question 1190317: A circle is inscribed in a right triangle that has a hypotenuse of 182 cm. If the perimeter of the triangle is 420 cm, what is the radius of the inscribed circle? \n" ); document.write( "

Algebra.Com's Answer #821933 by ikleyn(52802) $\"\"$ $\"About$

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\n" ); document.write( "A circle is inscribed in a right triangle that has a hypotenuse of 182 cm.
\n" ); document.write( "If the perimeter of the triangle is 420 cm, what is the radius of the inscribed circle?
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document.write( "For any right triangle, the radius of the inscribed circle is \r\n" );
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document.write( "    r = ,     (1)\r\n" );
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document.write( "where \"a\" and \"b\" are the legs lengths and \"c\" is the hypotenuse length.\r\n" );
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document.write( "We are given the perimeter P = a + b + c = 420 cm  and  the hypotenuse length  c= 182 cm,\r\n" );
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document.write( "therefore, we can easily compute the radius of the inscribed circle\r\n" );
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document.write( "    r =  =  =  = 210 - 182 = 28 centimeters.    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Regarding formula (1) and its proof, see the lesson\r
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\n" ); document.write( "\n" ); document.write( " - The radius of a circle inscribed into a right angled triangle\r
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