document.write( "Question 251162: A rectangle has a perimeter of 14 feet, and twice its length l is equal to two more than 4 times its width w. Find l and w. \n" ); document.write( "

Algebra.Com's Answer #184191 by oberobic(2304) $\"\"$ $\"About$

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Define your variables and list known items:
\n" ); document.write( "p = perimeter = 14
\n" ); document.write( "l = length
\n" ); document.write( "w = width
\n" ); document.write( "p = 2l + 2w = 2(l+w)
\n" ); document.write( "l = 4w + 2
\n" ); document.write( ".
\n" ); document.write( "substituting l = 4w+2 into the perimeter equation
\n" ); document.write( "14 = 2(4w+2) + 2w
\n" ); document.write( ".
\n" ); document.write( "multiply to remove the parentheses
\n" ); document.write( "14 = 8w +4 + 2w
\n" ); document.write( ".
\n" ); document.write( "collect terms
\n" ); document.write( "14 = 10w +4
\n" ); document.write( ".
\n" ); document.write( "subtract 4 from both sides
\n" ); document.write( "10 = 10w
\n" ); document.write( ".
\n" ); document.write( "divide both sides by 10
\n" ); document.write( "1 = w
\n" ); document.write( "w = 1
\n" ); document.write( ".
\n" ); document.write( "substituting back into l = 4w+2
\n" ); document.write( "l = 4(1) + 2 = 6
\n" ); document.write( ".
\n" ); document.write( "checking the perimeter
\n" ); document.write( "2l = 12
\n" ); document.write( "2w = 2
\n" ); document.write( "2l + 2w = 14, which is correct.
\n" ); document.write( ".
\n" ); document.write( "so our answer is:
\n" ); document.write( "l=4
\n" ); document.write( "w=1
\n" ); document.write( ".
\n" ); document.write( "done \n" ); document.write( "

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