document.write( "Question 1201846: A circular piece of sheet metal has a diameter of 20 in. The edges are to be cut off to form a rectangle of area 150 in2 (see the figure). What are the dimensions of the rectangle? (Round your answers to two decimal places.)
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Algebra.Com's Answer #836390 by ikleyn(52850) $\"\"$ $\"About$

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\n" ); document.write( "A circular piece of sheet metal has a diameter of 20 in.
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\n" ); document.write( "\n" ); document.write( " There is more simple solution to this problem (and, therefore, more preferable).\r
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document.write( "Let x is the longer side of the rectangle and y is its shorter side.\r\n" );
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document.write( "From the description, you have these two equations\r\n" );
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document.write( "    xy = 150           (1)  (the area)\r\n" );
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document.write( "    x^2 + y^ = 20^2    (2)  (the diagonal of the rectangle,\r\n" );
document.write( "                            which is the diameter of the circle)\r\n" );
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document.write( "Multiply equation (1) by 2 (both sides) and add to equation (2).  You will get\r\n" );
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document.write( "    x^2 + 2xy + z^2 = 700    (3)\r\n" );
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document.write( "Multiply equation (1) by 2 (both sides) and subtract from equation (2).  You will get\r\n" );
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document.write( "    x^2 - 2xy + z^2 = 100    (4)\r\n" );
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document.write( "Equations (3) and (4) are equivalent to this system of equations\r\n" );
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document.write( "    (x+y)^2 = 700\r\n" );
document.write( "    (x-y)^2 = 100\r\n" );
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document.write( "Taking square roots from both sides of these equations, you arrive to simple system of linear equations\r\n" );
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document.write( "    x + y = ,\r\n" );
document.write( "    x - y = 10.\r\n" );
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document.write( "or    \r\n" );
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document.write( "    x + y = ,     (5)\r\n" );
document.write( "    x - y = 10.         (6)\r\n" );
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document.write( "Add these equations to eliminate y.  You will get\r\n" );
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document.write( "    2x = ,  which implies  x = .\r\n" );
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document.write( "Subtract equation (6) from equation (5) to eliminate x.  You will get\r\n" );
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document.write( "    2y = ,  which implies  y = .\r\n" );
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document.write( "ANSWER.  x = ,  y = .\r\n" );
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