document.write( "Question 256885: The length of a rectangle is 2 centimeters less than twice its width. The perimeter of the rectangle is 32 cm. What are the dimensions of the rectangle? \n" ); document.write( "

Algebra.Com's Answer #188931 by EMStelley(208) $\"\"$ $\"About$

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Let's start by naming variables. Let's call the length L and the width W. Then the first sentence tell us that:\r
\n" ); document.write( "\n" ); document.write( "L = 2W - 2\r
\n" ); document.write( "\n" ); document.write( "Remember that the perimeter of a rectangle is P = 2L + 2W. So the second sentence tells us:\r
\n" ); document.write( "\n" ); document.write( "2L + 2W = 32\r
\n" ); document.write( "\n" ); document.write( "Now, in order to solve these two equations, notice that we can use the first equation to replace L with 2W - 2. This gives us:\r
\n" ); document.write( "\n" ); document.write( "2(2W - 2) + 2W = 32
\n" ); document.write( "4W - 4 + 2W = 32
\n" ); document.write( "6W - 4 = 32
\n" ); document.write( "6W = 36
\n" ); document.write( "W = 6\r
\n" ); document.write( "\n" ); document.write( "So the width is 6 cm. To finish the problem, we need to find the length, so let's substitute 6 in for W in the first equation:\r
\n" ); document.write( "\n" ); document.write( "L = 2(6) - 2
\n" ); document.write( "L = 12 - 2
\n" ); document.write( "L = 10\r
\n" ); document.write( "\n" ); document.write( "So the dimensions of the rectangle are 10 cm by 6 cm. \n" ); document.write( "

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