document.write( "Question 64953: My son is trying to find the length from the top left corner to the bottom right corner of a cube.\r
\n" ); document.write( "\n" ); document.write( "This is something I have not been taught, and have tried to find the formula on the internet, without success.\r
\n" ); document.write( "\n" ); document.write( "For example, how would this be done for a cube with the dimensions 3.3m x 1.7m x 1.7m\r
\n" ); document.write( "\n" ); document.write( "Regards\r
\n" ); document.write( "\n" ); document.write( "Gordon \n" ); document.write( "

Algebra.Com's Answer #45433 by Edwin McCravy(20063) $\"\"$ $\"About$

You can put this solution on YOUR website!
There's an error in Stan's solution above. He has\r
\n" ); document.write( "\n" ); document.write( "D^2=10.89 + 1.7sqrt2 <--That should be D^2=10.89 + (1.7sqrt2)^2
\n" ); document.write( "D^2=13.29 <--That should be 16.67
\n" ); document.write( "D=sqrt13.29 <--That should be sqrt16.67
\n" ); document.write( "D=3.646.. <--That should be 4.08289...\r
\n" ); document.write( "\n" ); document.write( "Here's my explanation:\r
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My son is trying to find the length from the top left\r\n" );
document.write( "corner to the bottom right corner of a cube. \r\n" );
document.write( "This is something I have not been taught, and have \r\n" );
document.write( "tried to find the formula on the internet, without success.\r\n" );
document.write( "For example, how would this be done for a cube with the \r\n" );
document.write( "dimensions 3.3m x 1.7m x 1.7m \r\n" );
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document.write( "First of all, the dimensions 3.3m x 1.7m x 1.7m, cannot \r\n" );
document.write( "apply to a cube, because to be correctly called a \"cube\", \r\n" );
document.write( "all 6 of its faces must be congruent squares.  \r\n" );
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document.write( "Now either of the dimensions 1.7m x 1.7m x 1.7m or the dimensions\r\n" );
document.write( "3.3m x 3.3m x 3.3m could apply to a cube, but not the dimensions \r\n" );
document.write( "3.3m x 1.7m x 1.7m. \r\n" );
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document.write( "The dimensions 3.3m x 1.7m x 1.7m could only apply to a \r\n" );
document.write( "rectangular solid, two of the faces of which are 1.7m x 1.7m \r\n" );
document.write( "squares and the other four faces 3.3m x 1.7m rectangles.\r\n" );
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document.write( "Anyway, with the semantics of the word \"cube\" out of the way, I \r\n" );
document.write( "will answer your question about the longest possible rigid rod \r\n" );
document.write( "that could fit inside a 3.3m x 1.7m x 1.7m rectangular solid \r\n" );
document.write( "without bending the rod, that is, the distance from A to G\r\n" );
document.write( "in the drawing below:\r\n" );
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document.write( "   A____B  \r\n" );
document.write( "   |\D__\C     \r\n" );
document.write( "  E||   |    <--(H is back behind, below B, right of E, and behind G.     \r\n" );
document.write( "   \|___|        You can't see H in the picture.   \r\n" );
document.write( "   F    G \r\n" );
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document.write( "Suppose AB = BC = CD = DA = FG = GH = HE = EF = 1.7m\r\n" );
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document.write( "Suppose AE = BH = CG = DF = 3.3m\r\n" );
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document.write( "You want to find AG. Plan:\r\n" );
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document.write( "1. Draw (or think of drawing) AC. Then ABC is a right triangle\r\n" );
document.write( "2. Find AC² using AC² = AB²+BC²   \r\n" );
document.write( "3. Draw (or think of drawing) AG. Then ACG is a right triangle\r\n" );
document.write( "4. Find AG² using AG² = AC²+CG²\r\n" );
document.write( "5. Find AG by taking the square root of AG² \r\n" );
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document.write( "AC² = AB² + BC²\r\n" );
document.write( "AC² = 1.7² + 1.7² = 5.78\r\n" );
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document.write( "AG² = AC² + CG²\r\n" );
document.write( "AG² = 5.78 + 3.3² = 16.67\r\n" );
document.write( "      _____\r\n" );
document.write( "AG = Ö16.67 = 4.082891133 approximately  \r\n" );
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document.write( "Edwin

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