document.write( "Question 204754: The length of a rectangle is 7 m more than the width. The length of a diagonal is 13 m. Find the length. \n" ); document.write( "

Algebra.Com's Answer #154551 by alicealc(293) $\"\"$ $\"About$

You can put this solution on YOUR website!
rectangle's length = L
\n" ); document.write( "rectangle's width = W
\n" ); document.write( "rectangle's diagonal = D\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "L = 7 + W
\n" ); document.write( "D = 13
\n" ); document.write( "use the Phytagoras formula:
\n" ); document.write( " $\"D%5E2+=+L%5E2+%2B+W%5E2\"$
\n" ); document.write( " $\"13%5E2+=+%287+%2B+W%29%5E2+%2B+W%5E2\"$
\n" ); document.write( " $\"169+=+49+%2B+14W+%2B+W%5E2+%2B+W%5E2\"$
\n" ); document.write( " $\"0+=+49+%2B+14W+%2B+W%5E2+%2B+W%5E2+-+169\"$
\n" ); document.write( " $\"0+=+2W%5E2+%2B+14W+%2B+-+120\"$
\n" ); document.write( "divide each side by 2
\n" ); document.write( " $\"0+=+W%5E2+%2B+7W+%2B+-+60\"$
\n" ); document.write( "factorize it:
\n" ); document.write( "0 = (W + 12)(W - 5)
\n" ); document.write( "W + 12 = 0 --> W = -12
\n" ); document.write( "or
\n" ); document.write( "W - 5 = 0 --> W = 5\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "W = 5 is used because the width of a rectangle must not be a negative value
\n" ); document.write( "L = 7 + W = 7 + 5 = 12\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "so, the length of the rectangle is 12 m \r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );