document.write( "Question 832540: A triangle has sides with lengths of 5 meters, 11 meters, and 12 meters. Is it a right triangle? \n" ); document.write( "

Algebra.Com's Answer #502097 by math-vortex(648) $\"\"$ $\"About$

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document.write( "Hi, there--\r\n" );
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document.write( "THE PROBLEM:\r\n" );
document.write( "A triangle has sides with lengths of 5 meters, 11 meters, and 12 meters. Is it a right triangle?\r\n" );
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document.write( "A SOLUTION:\r\n" );
document.write( "We use the Pythagorean Theorem and its converse to determine if this triangle is a right triangle.\r\n" );
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document.write( "Together these two theorems show that: \"The square of one side of a triangle is equal to the sum of the \r\n" );
document.write( "squares of the other two sides, if and only if the triangle is a right triangle.\"\r\n" );
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document.write( "This is that famous equation  you have probably heard of.\r\n" );
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document.write( "We have a triangle with sides of lengths 5m, 11m, and 12m. If this is a right triangle, then the longest \r\n" );
document.write( "must be the hypotenuse (the side labeled c.) The other two sides are the legs (sides labeled a and b.)\r\n" );
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document.write( "We will let \r\n" );
document.write( "a = 5m\r\n" );
document.write( "b = 11m\r\n" );
document.write( "c = 12m\r\n" );
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document.write( "If this triangle is a right triangle then the sum of the squares of a and b will equal the square of c.\r\n" );
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document.write( "Substitute these values into the Pythagorean Equation.\r\n" );
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document.write( "Now simplify each side of the equation and see if you have a true statement.\r\n" );
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document.write( "We see that the two sides of the equation are not equal, and the equation is FALSE.\r\n" );
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document.write( "The sum of the squares of two sides is not equal to the square of the other sides. Therefore, this triangle \r\n" );
document.write( "is NOT a right triangle.\r\n" );
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document.write( "Hope this helps! Feel free to email if you have any questions about the solution.\r\n" );
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document.write( "Good luck with your math,\r\n" );
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document.write( "Mrs. F\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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