document.write( "Question 825612: Find the length of side c of a triangle if side a = 15 and side b = 20.
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Algebra.Com's Answer #497485 by math-vortex(648)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Hi, there--\r\n" );
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document.write( "PROBLEM:\r\n" );
document.write( "Find the length of side c of a triangle if side a = 15 and side b = 20.\r\n" );
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document.write( "A SOLUTION:\r\n" );
document.write( "Is this a right triangle? If yes, then use the Pythagorean Equation \"a%5E2%2Bb%5E2=c%5E2\" where \r\n" );
document.write( "\"a\" and \"b\" are the lengths of the legs of your triangle, and \"c\" is the length of the \r\n" );
document.write( "hypotenuse (the longest side.) The hypotenuse is the side across from the right triangle.\r\n" );
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document.write( "Assuming that c is the length of the hypotenuse in your triangle, substitute 15 for a and 20 \r\n" );
document.write( "for b.\r\n" );
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document.write( "\"%2815%29%5E2%2B%2820%29%5E2=c%5E2\"\r\n" );
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document.write( "Simplify.\r\n" );
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document.write( "\"225%2B400=c%5E2\"\r\n" );
document.write( "\"625=c%5E2\"\r\n" );
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document.write( "We know that c^2 (c times itself) equals 625. We want to know what c is, so we take \r\n" );
document.write( "the square root of both sides. ( The square root of c^2 is c because c*c=c^2. The square root \r\n" );
document.write( "of 625 is 25 because 25*25=625.)\r\n" );
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document.write( "\"c=25\"\r\n" );
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document.write( "The length of c is 25 if the triangle is a right triangle and c is the hypotenuse.\r\n" );
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document.write( "If your triangle is not a right triangle, then there are many correct answers. Use the Triangle \r\n" );
document.write( "Inequality which states that for any triangle, the sum of the lengths of any two sides must be \r\n" );
document.write( "greater than the length of the remaining side.\r\n" );
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document.write( "In your triangle, all the following must be true: 15 + 20 > c, and c + 15 > 20, and c + 20 > 15\r\n" );
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document.write( "Solve each inequality:\r\n" );
document.write( "15 + 20 > c\r\n" );
document.write( "35 > c\r\n" );
document.write( "c < 35\r\n" );
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document.write( "c + 15 > 20\r\n" );
document.write( "c > 20 - 15\r\n" );
document.write( "c > 5\r\n" );
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document.write( "c + 20 > 15\r\n" );
document.write( "c > 15 - 20\r\n" );
document.write( "c > -5\r\n" );
document.write( "No additional information is gained here. A side length cannot be negative, and we already know from the second inequality that c > 5.\r\n" );
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document.write( "Therefore, 5 < c < 35\r\n" );
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document.write( "The length of c can be any positive number that is greater than 5 and less than 35.\r\n" );
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document.write( "Hope this helps!\r\n" );
document.write( "Mrs. Figgy\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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