document.write( "Question 1099076: the length of a rectangle is 18 cm more than the width. A second rectangle is 6cm shorter and 3cm wider than the first and has a perimeter of 126cm. find the dimensions of each rectangle
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Algebra.Com's Answer #713481 by ikleyn(52787) $\"\"$ $\"About$

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document.write( "Let L and W are the length and the width of the first rectangle ( in centimeters).\r\n" );
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document.write( "Then from the condition, you have this equation \r\n" );
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document.write( "L - W = 18.       (1)\r\n" );
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document.write( "The second rectangle has the dimensions (L-6) and (W+3), according to the condition.\r\n" );
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document.write( "Hence, its perimeter is  2*(L-6) + 2*(W+3), and you have the second equation\r\n" );
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document.write( "2*(L-6) + 2*(W+3) = 126,    or, equivalently,   L-6 + W+3 = 63,  or, equivalently,\r\n" );
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document.write( "L + W = 66.       (2)\r\n" );
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document.write( "Thus from the condition you have the system of two equations (1) and (2). To solve it, add the equations. You will get\r\n" );
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document.write( "2L = 18 + 66 = 84  ====>  L =  = 42.\r\n" );
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document.write( "Thus the length of the first rectangle is 42 cm.\r\n" );
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document.write( "Then its width is  42-18 = 24 cm.\r\n" );
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document.write( "The dimension of the other rectangle are 42-6 = 36 cm  and  24+3 = 27 cm.\r\n" );
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