document.write( "Question 286489: the perimeter of a rectangle is 74 inches. If the width is doubled and the length is halved, the new rectangle will have a perimeter is 76 inches. What are the dimensions? \n" ); document.write( "

Algebra.Com's Answer #207788 by texttutoring(324) $\"\"$ $\"About$

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You have two unknowns, l=length and w=width, so you need two equations.\r
\n" ); document.write( "\n" ); document.write( "Recall that perimeter of a rectangle is P = 2l + 2w\r
\n" ); document.write( "\n" ); document.write( "Eqn 1: 74 = 2w + 2l
\n" ); document.write( "Eqn 2: 76 = 2(2w) + 2l/2
\n" ); document.write( " 76 = 4w +l\r
\n" ); document.write( "\n" ); document.write( "Rearrange Eqn. 2, isolating for l:\r
\n" ); document.write( "\n" ); document.write( "l=76-4w\r
\n" ); document.write( "\n" ); document.write( "Insert this expression for l into Eqn 1:\r
\n" ); document.write( "\n" ); document.write( "74 = 2w + 2(76-4w)
\n" ); document.write( "74 = 2w + 152 -8w
\n" ); document.write( "6w = 78
\n" ); document.write( "w=13\r
\n" ); document.write( "\n" ); document.write( "The length can be found from either Eqn1 or 2:\r
\n" ); document.write( "\n" ); document.write( "l = 76-4w
\n" ); document.write( "l = 76-4(13)
\n" ); document.write( "l=24\r
\n" ); document.write( "\n" ); document.write( "So the width is 13 and the length is 24.\r
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\n" ); document.write( "\n" ); document.write( "Let me know if you have any questions about this solution. \n" ); document.write( "

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