document.write( "Question 1151211: The length of each side of a square is 3 in. more than the length of each side of a smaller square. The sum of the areas of the squares is 45 in squared . Find the lengths of the sides of the two squares. \n" ); document.write( "

Algebra.Com's Answer #772874 by ikleyn(52788) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "From the condition, you have this system of 2 equations\r\n" );
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document.write( "    x - y = 3              (1)\r\n" );
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document.write( "    x^2 + y^2 = 45.        (2)\r\n" );
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document.write( "Square equation (1); keep equation (2) as is.\r\n" );
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document.write( "    x^2 - 2x + y^2 = 9     (1')\r\n" );
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document.write( "    x^2      + y^2 = 45    (2')\r\n" );
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document.write( "Now subtract equation (1') from equation (1'). You will get\r\n" );
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document.write( "         2xy       = 45 - 9 = 36,   or\r\n" );
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document.write( "          xy                = 36/2 = 18.\r\n" );
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document.write( "Thus you have two numbers x and y  with the difference of 3 and the product of 18.\r\n" );
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document.write( "3 seconds is enough to guess (to recognize) these numbers,  3 and 6.\r\n" );
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