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Three times the width of a certain rectangle exceeds twice its length by three inches, and four times its length is twelve more than its perimeter. Find the dimensions of the rectangle.
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\n" ); document.write( "Take it step-by-step, write an equation each statement:
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\n" ); document.write( "\"Three times the width of a certain rectangle exceeds twice its length by three inches,\"
\n" ); document.write( "3W = 2L + 3
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\n" ); document.write( "\" four times its length is twelve more than its perimeter.\"
\n" ); document.write( "4L = 12 + (2L+2W)
\n" ); document.write( "4L = 12 + 2L + 2W
\n" ); document.write( "4L - 2L = 12 + 2W
\n" ); document.write( "2L = 12 + 2W
\n" ); document.write( "Simplify divide by 2
\n" ); document.write( "L = W + 6
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\n" ); document.write( "In the 1st equation (3W = 2L+3) substitute (W+6) for L
\n" ); document.write( "3W = 2(W+6) + 3
\n" ); document.write( "3W = 2W + 12 + 3
\n" ); document.write( "3W - 2W = 15
\n" ); document.write( "W = 15
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\n" ); document.write( "Find L
\n" ); document.write( "L = 15 + 6
\n" ); document.write( "L = 21
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\n" ); document.write( "See if this is true in statement:
\n" ); document.write( "\"Three times the width of a certain rectangle exceeds twice its length by three\"
\n" ); document.write( "3(15) = 2(21) + 3
\n" ); document.write( "45 = 42 + 3
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\n" ); document.write( "See if you can prove it in the statement:
\n" ); document.write( "\"four times its length is twelve more than its perimeter.\"
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\n" ); document.write( "Did the explain it clearly to you? Let me know. \n" ); document.write( "