document.write( "Question 1096586: if the length of the rectangle is reduced by 5 units and its breadth is increased by 3 units then the area of rectangle is reduced by 8 square units. if length is reduced by 3 units and breadth is increased by 2 units, then the area of rectangle will increase by 6 7 square units. Then find the length and breadth of the rectangle. \n" ); document.write( "
Algebra.Com's Answer #711032 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
I am going to ignore the 7 in the last sentence
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\n" ); document.write( "Write an equation for each and reduce to a simple 2 unknown equation
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\n" ); document.write( " if the length of the rectangle is reduced by 5 units and its breadth is increased by 3 units then the area of rectangle is reduced by 8 square units.
\n" ); document.write( "(L-5)(w+3) = LW - 8
\n" ); document.write( "FOIL
\n" ); document.write( "LW + 3L - 5w - 15 = LW - 8
\n" ); document.write( "LW - LW + 3L - 5W = 15 - 8
\n" ); document.write( "3L - 5w = 7
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\n" ); document.write( " if length is reduced by 3 units and breadth is increased by 2 units, then the area of rectangle will increase by 6 square units.]
\n" ); document.write( "(L-3)(w+2) = Lw + 6
\n" ); document.write( "Lw + 2L - 3w - 6 = Lw + 6
\n" ); document.write( "Lw - Lw + 2L - 3w = 6 + 6
\n" ); document.write( "2L - 3w = 12
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\n" ); document.write( "Using these two equations
\n" ); document.write( "3L + 5w = 7
\n" ); document.write( "2L - 3w = 12
\n" ); document.write( "multiply the 1st by 2 and the 2nd by 3
\n" ); document.write( "6L + 10w = 14
\n" ); document.write( "6L - 9w = 36
\n" ); document.write( "----------------subtraction eliminates L find w
\n" ); document.write( "0 - w = - 22
\n" ); document.write( "w = 22 units is the width
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\n" ); document.write( "Find the Length using the 1st equation
\n" ); document.write( "2L - 3(22) = 12
\n" ); document.write( "2L - 66 = 12
\n" ); document.write( "2L = 12 + 66
\n" ); document.write( "2L - 78
\n" ); document.write( "L = 78/2
\n" ); document.write( "L = 39 units is length
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\n" ); document.write( "Find the original area: 39 * 22 = 858 sq units
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\n" ); document.write( "see if this checks out in the statement:
\n" ); document.write( "\" if the length of the rectangle is reduced by 5 units and its breadth is increased by 3 units then the area of rectangle is reduced by 8 square units.
\n" ); document.write( "(39-5) * (22+3) = 858 - 8
\n" ); document.write( "34 * 25 = 850
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\n" ); document.write( "You can check for yourself in the 2nd statement\r
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