document.write( "Question 1189165: Dear Colleagues\r
\n" ); document.write( "\n" ); document.write( "I have the following question to find a solution to:
\n" ); document.write( "The length of a rectangle exceeds its breadth by 4 centimetres. If the length were halved and the breadth increased by 5 centimetres, the area would be decreased by 35 square centimetres. Find the length of the rectangle.\r
\n" ); document.write( "\n" ); document.write( "I do not know if I can draw in this website, but whilst trying to find the solutions, I drew 2 rectangles: the one on the left had the dimensions (x)(x+4) for width and length respectively, the one on the right had dimensions ((x+4)/2)(x+5) for length and width respectively.
\n" ); document.write( "The question then reads - for me - [((x+4)/2)(x+5)] - 35 = x(x+4)
\n" ); document.write( "Multiplying the left hand by 2 to clear the fraction, we get
\n" ); document.write( "[(x+4)(2x+10)]-35 = x(x+4)
\n" ); document.write( "and after multiplying out we get
\n" ); document.write( "[2x^2+10x+8x+40]-35 = x^2+4x
\n" ); document.write( "Collecting like terms gives us
\n" ); document.write( "2x^2+18x+5 = x^2+4x
\n" ); document.write( "which simplifies to
\n" ); document.write( "x^2+14x+5=0
\n" ); document.write( "We cannot factorise, so using the quadratic formula we get
\n" ); document.write( "a = 1, b= 14, c = 5
\n" ); document.write( "and putting all of this into the formula we get\r
\n" ); document.write( "\n" ); document.write( "x = (-b+/- sqrt of b^2-4ac)/2
\n" ); document.write( "which gives
\n" ); document.write( "x = (-14 +/- sqrt (14)^2-(4)(1)(5))/2\r
\n" ); document.write( "\n" ); document.write( "which gives us, finally, x = (-14 +/-13.23)/2\r
\n" ); document.write( "\n" ); document.write( "I am assuming that we need a real number for the length of the side of the rectangle, so do not wish to get into imaginary numbers...
\n" ); document.write( "Where have I gone wrong? \n" ); document.write( "

Algebra.Com's Answer #820482 by MathTherapy(10552) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "Dear Colleagues\r
\n" ); document.write( "\n" ); document.write( "I have the following question to find a solution to:
\n" ); document.write( "The length of a rectangle exceeds its breadth by 4 centimetres. If the length were halved and the breadth increased by 5 centimetres, the area would be decreased by 35 square centimetres. Find the length of the rectangle.\r
\n" ); document.write( "\n" ); document.write( "I do not know if I can draw in this website, but whilst trying to find the solutions, I drew 2 rectangles: the one on the left had the dimensions (x)(x+4) for width and length respectively, the one on the right had dimensions ((x+4)/2)(x+5) for length and width respectively.
\n" ); document.write( "The question then reads - for me - [((x+4)/2)(x+5)] - 35 = x(x+4)
\n" ); document.write( "Multiplying the left hand by 2 to clear the fraction, we get
\n" ); document.write( "[(x+4)(2x+10)]-35 = x(x+4)
\n" ); document.write( "and after multiplying out we get
\n" ); document.write( "[2x^2+10x+8x+40]-35 = x^2+4x
\n" ); document.write( "Collecting like terms gives us
\n" ); document.write( "2x^2+18x+5 = x^2+4x
\n" ); document.write( "which simplifies to
\n" ); document.write( "x^2+14x+5=0
\n" ); document.write( "We cannot factorise, so using the quadratic formula we get
\n" ); document.write( "a = 1, b= 14, c = 5
\n" ); document.write( "and putting all of this into the formula we get\r
\n" ); document.write( "\n" ); document.write( "x = (-b+/- sqrt of b^2-4ac)/2
\n" ); document.write( "which gives
\n" ); document.write( "x = (-14 +/- sqrt (14)^2-(4)(1)(5))/2\r
\n" ); document.write( "\n" ); document.write( "which gives us, finally, x = (-14 +/-13.23)/2\r
\n" ); document.write( "\n" ); document.write( "I am assuming that we need a real number for the length of the side of the rectangle, so do not wish to get into imaginary numbers...
\n" ); document.write( "Where have I gone wrong?
\n" ); document.write( "

The first error you made was forming an incorrect equation. \r\n" );
document.write( "The easiest way to do this problem is to let the variable be what's asked for.\r\n" );
document.write( "In other words, let the original length (requested value) be L\r\n" );
document.write( "Then the breadth is L - 4\r\n" );
document.write( "Halving the length gives the new length, \r\n" );
document.write( "Increasing the breadth by 5 gives the new breadth, L - 4 + 5, or L + 1\r\n" );
document.write( "Original area: L(L - 4)\r\n" );
document.write( "Given that the original area is reduced by 35, we get: \r\n" );
document.write( "                 ------ Multiplying by LCD, 2\r\n" );
document.write( "           \r\n" );
document.write( "       (L - 14)(L + 5) = 0\r\n" );
document.write( "                L - 14 = 0            or      L + 5 = 0 \r\n" );
document.write( "Original length, or       or      L = - 5 (ignore)

\n" ); document.write( "

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