document.write( "Question 1172178: 3. A picture 8 in. by 12 in. is placed in a frame which has a uniform width. If the area of the frame is equal to the area of the picture, find the width of the frame. Show clear solutions thanksss! \n" ); document.write( "

Algebra.Com's Answer #797113 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "Let the uniform width of the frame be \" x \" inches.\r\n" );
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document.write( "Then the outer dimensions of the frame are  8+2x and 12+2x.\r\n" );
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document.write( "From the condition, you have this equation\r\n" );
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document.write( "    (8+2x)*(12+2x) - 8*12 = 8*12.\r\n" );
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document.write( "Reduce it to the standard form quadratic equation\r\n" );
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document.write( "    96 + 16x + 24x + 4x^2 - 96 = 96\r\n" );
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document.write( "    4x^2 + 40x - 96 = 0\r\n" );
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document.write( "     x^2 + 10x - 24 = 0\r\n" );
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document.write( "     (x+12)*(x-2) = 0.\r\n" );
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document.write( "This equation has two root, -12 and 2.\r\n" );
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document.write( "Of them , only positive value makes sense.\r\n" );
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document.write( "ANSWER.  The uniform width of the frame is  2 inches.\r\n" );
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