document.write( "Question 1021571: the legs of a right triangle are in the ratio 3:4 and its area is 1014 cm^2. find the length and perimeter \n" ); document.write( "

Algebra.Com's Answer #637308 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "the legs of a right triangle are in the ratio 3:4 and its area is 1014 cm^2. find the length and perimeter
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document.write( "It is 3:4:5 right-angled triangle.\r\n" );
document.write( "   (If in a right-angled triangle the two legs are in the ratio 3:4, then the hypotenuse is 5 units long. \r\n" );
document.write( "    Everybody knows it).\r\n" );
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document.write( "So, the length of one leg is 3 units, the length of the second leg is 4 units, and the length of the hypotenuse is 5 units.\r\n" );
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document.write( "Then the area of the triangle is half the product of its legs measures, i.e.  = , \r\n" );
document.write( "where x is the length of that unit.\r\n" );
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document.write( "From the condition, you know that the area is 1014 .\r\n" );
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document.write( "It gives you an equation\r\n" );
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document.write( " = .\r\n" );
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document.write( "Hence,   =  = 169   and   x = 13 cm.\r\n" );
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document.write( "Now one leg is 3*13 = 39 cm,  the other leg is  4*13 = 52 cm,  and the hypotenuse is  5*13 = 65 cm.\r\n" );
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document.write( "Thus the perimeter = 39 + 52 + 65 = 156 cm\r\n" );
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