document.write( "Question 1205620: Here is a solution by MathLover1:
\n" ); document.write( "http://www.algebra.com/tutors/students/your-answer.mpl?question=1205618\r
\n" ); document.write( "\n" ); document.write( "I would never in a million years trust her solution, given her reputation on this forum. Can someone either verify, or provide the right solution?\r
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Algebra.Com's Answer #842529 by ikleyn(52781) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( "Point X is the intersection of the two diagonals TW and UV of the cubical box illustrated.
\n" ); document.write( "The shortest distance from point T to point Z is $\"4sqrt%283%29\"$ cm.
\n" ); document.write( "Find the area in square centimetres of triangle XYZ.
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document.write( "It is well known fact that if \"a\" is the length of the edge of a cube,\r\n" );
document.write( "then the longest 3D-diagonal of the cube, connecting the opposite corners (vertices)\r\n" );
document.write( "is  .\r\n" );
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document.write( "In this problem, you are given that the longest 3D-diagonal of the cube is  cm.\r\n" );
document.write( "It means that the edge of the cube is 4 cm long.\r\n" );
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document.write( "OK.  To find the area of triangle XYZ, we need to know its height (its altitude).\r\n" );
document.write( "This altitude is the hypotenuse of the right angled triangle with the legs a/2 = 2 cm\r\n" );
document.write( "and a = 4 cm, so the altitude of the triangle XYZ is\r\n" );
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document.write( "    h =  =  =  cm.\r\n" );
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document.write( "Now the area of the triangle XYZ is half the product of its base a = ZY = 4 cm by the altitude h\r\n" );
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document.write( "     =  =  = 8.944 cm^2  (approximately).    ANSWER\r\n" );
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