document.write( "Question 418292: the length of a rectangle is 4 meters less than 3 times the width. If the perimeter is 56 meters, find the length and width of the rectangle. \n" ); document.write( "

Algebra.Com's Answer #292755 by oberobic(2304) $\"\"$ $\"About$

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Start by turning the words into equations.
\n" ); document.write( "l = length
\n" ); document.write( "w = width
\n" ); document.write( "length = 3*width - 4
\n" ); document.write( "l = 3*w - 4
\n" ); document.write( ".
\n" ); document.write( "P = perimeter = 2(l+w) = 2l + 2w, which is a known equation for a rectangle.
\n" ); document.write( "P = 56 is given
\n" ); document.write( "2l + 2w = 56
\n" ); document.write( ".
\n" ); document.write( "Substituting what we know l equals.
\n" ); document.write( ".
\n" ); document.write( "2(3w-4) + 2w = 56
\n" ); document.write( ".
\n" ); document.write( "Multiply by 2 to remove the parenthesis.
\n" ); document.write( ".
\n" ); document.write( "6w - 8 + 2w = 56
\n" ); document.write( ".
\n" ); document.write( "Collect terms
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\n" ); document.write( "8w - 8 = 56
\n" ); document.write( ".
\n" ); document.write( "Add 8 to both sides
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\n" ); document.write( "8w = 64
\n" ); document.write( ".
\n" ); document.write( "Divide both sides by 8
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\n" ); document.write( "w = 8 = width
\n" ); document.write( ".
\n" ); document.write( "Looking back, we see
\n" ); document.write( "l = 3w -4 = 3(8) - 4 = 24 - 4 = 20 = length
\n" ); document.write( ".
\n" ); document.write( "Always check your work. In this case, if the width = 8 and the length = 20, is the perimeter 56?
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\n" ); document.write( "2(20)+2(8) = 40 + 16 = 56.
\n" ); document.write( "Yes it is.
\n" ); document.write( ".
\n" ); document.write( "Remember to state the answer.
\n" ); document.write( "The length=20 and the width=8.
\n" ); document.write( ".
\n" ); document.write( "Done. \n" ); document.write( "

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