document.write( "Question 168855: A rod of unknown length is used to measure the dimensions of a rectangular door. The rod is 4 ch'ih longer than the width of the door. The rod is 2 ch'ih longer than the height of the door, ad the same length as the door's diagonal. What are the dimensions of the door? \n" ); document.write( "

Algebra.Com's Answer #124516 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Call the length of the rod $\"x\"$
\n" ); document.write( "given:
\n" ); document.write( "The width is $\"x+-+4\"$
\n" ); document.write( "The length is $\"x+-+2\"$
\n" ); document.write( "The diagonal is $\"x\"$
\n" ); document.write( " $\"%28x+-+4%29%5E2+%2B+%28x+-+2%29%5E2+=+x%5E2\"$
\n" ); document.write( " $\"x%5E2+-+8x+%2B+16+%2B+x%5E2+-+4x+%2B+4+=+x%5E2\"$
\n" ); document.write( " $\"x%5E2+-+12x+%2B+20+=+0\"$
\n" ); document.write( " $\"%28x+-+10%29%2A%28x+-+2%29+=+0\"$
\n" ); document.write( "There are 2 solutions
\n" ); document.write( " $\"x+=+2\"$
\n" ); document.write( "This is impossible because $\"x+-+2+=+0\"$ and $\"x+-+4+=+-2\"$
\n" ); document.write( " $\"x+=+10\"$ answer
\n" ); document.write( " $\"x+-+2+=+8\"$
\n" ); document.write( " $\"x+-+4+=+6\"$
\n" ); document.write( "The dimensions of the door are 6x8
\n" ); document.write( "check:
\n" ); document.write( " $\"%28x+-+4%29%5E2+%2B+%28x+-+2%29%5E2+=+x%5E2\"$
\n" ); document.write( " $\"%2810+-+4%29%5E2+%2B+%2810+-+2%29%5E2+=+10%5E2\"$
\n" ); document.write( " $\"6%5E2+%2B+8%5E2+=+10%5E2\"$
\n" ); document.write( " $\"36+%2B+64+=+100\"$
\n" ); document.write( " $\"100+=+100\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );