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You can put this solution on YOUR website!
To solve problems like these you have to make an equation from the information given.
\n" ); document.write( "Let's call the length x.
\n" ); document.write( "Because the width is 3 less than the length, we can say that....
\n" ); document.write( "the width is (x-3).
\n" ); document.write( "We know that area = length x width. So now we can write
\n" ); document.write( "54 = x*(x-3).
\n" ); document.write( "Multiplying out the brackets gives
\n" ); document.write( "54 =
\n" ); document.write( "rearranging this gives
\n" ); document.write( "
\n" ); document.write( "So we have a quadratic equation which will have 2 solutions.
\n" ); document.write( "To find what they are we have to find factors of -54. These are plus/minus 1 and 54, plus/minus 2 and 27, plus/minus 3 and 18, plus/minus 6 and 9.
\n" ); document.write( "Because there is -3x in the quadratic equation we are looking for factors which we can add or take to make to make -3.
\n" ); document.write( "Obviously, the factors we must choose are +6 and -9, these will multiply to make -54 and we can add them to make -3.
\n" ); document.write( "We will use those factors to factorise the equation
\n" ); document.write( "Thus we get
\n" ); document.write( "(x+6)(x-9) = 0
\n" ); document.write( "because one of these factors must equal 0 we can say that either
\n" ); document.write( "(x+6) = 0 OR (x-9) = 0
\n" ); document.write( "solving these linear equations gives
\n" ); document.write( "x = -6, OR x = 9
\n" ); document.write( "The first solution is nonsense as you can't have a negative measurement
\n" ); document.write( "so the length of the rectangle is 9 cm.
\n" ); document.write( "Hope that helps. \n" ); document.write( "