document.write( "Question 633612: the length of a rectangle is 1m longer than twice the width. the area of the rectangle is 105m squared find the length and the width of the rectangle \n" ); document.write( "

Algebra.Com's Answer #399019 by Earlsdon(6294) $\"\"$ $\"About$

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Let L = length and W = width.
\n" ); document.write( " $\"L+=+2W%2B1\"$ \"The length of a rectangle is 1m longer than twice the width.\"
\n" ); document.write( "The area of a rectangle is given by:
\n" ); document.write( " $\"A+=+L%2AW\"$ Substitute $\"L+=+2W%2B1\"$ and $\"A+=+105\"$ .
\n" ); document.write( " $\"105+=+%282W%2B1%29%2AW\"$ Simplify.
\n" ); document.write( " $\"105+=+2W%5E2%2BW\"$ Subtract 105 from both sides.
\n" ); document.write( " $\"2W%5E2%2BW-105+=+0\"$ Solve this quadratic equation by factoring.
\n" ); document.write( " $\"%282W%2B15%29%28W-7%29+=+0\"$ Apply the \"zero product\" rule.
\n" ); document.write( " $\"2W%2B15+=+0\"$ or $\"W-7+=+0\"$
\n" ); document.write( " $\"2W+=+-15\"$ or $\"W+=+7\"$ Discard the negative solution as the width, W is a positive quantity.
\n" ); document.write( " $\"W+=+7\"$ and $\"L+=+2%287%29%2B1\"$ = $\"15\"$ \n" ); document.write( "

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