document.write( "Question 90934: Hello, \r
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\n" ); document.write( "\n" ); document.write( "The length of a picture is one inch less than twice its width. The frame around the picture has a uniform width of two inches and an area of 96 square inches. What are the dimensions of the picture? \n" ); document.write( "
Algebra.Com's Answer #66062 by ankor@dixie-net.com(22740)\"\" \"About 
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The length of a picture is one inch less than twice its width. The frame around the picture has a uniform width of two inches and an area of 96 square inches. What are the dimensions of the picture?
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\n" ); document.write( "Let x = width of the picture
\n" ); document.write( "then
\n" ); document.write( "(2x-1) = length of the picture
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\n" ); document.write( "It would help to draw a rough diagram of this. Label the picture dimensions as
\n" ); document.write( "x and (2x-1). Label the uniform width around the picture as 2 inches. It will be
\n" ); document.write( "apparent that the overall dimensions of the frame will be 2x+3, (from 2x-1+4) and x+4.
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\n" ); document.write( "The overall dimensions would be (2x+3) by (x+4), it's area is given as: 96 sq/in
\n" ); document.write( "Length time width = area. Therefore:
\n" ); document.write( "(2x + 3)*(x+4) = 96
\n" ); document.write( "FOIL
\n" ); document.write( "2x^2 + 11x + 12 = 96
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\n" ); document.write( "2x^2 + 11x + 12 - 96 = 0
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\n" ); document.write( "2x^2 + 11x - 84 = 0; a quadratic equation
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\n" ); document.write( "Use the quadratic formula to find x: a=2; b=11; c=-84
\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"
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\n" ); document.write( "\"x+=+%28-11+%2B-+sqrt%28+11%5E2+-+4+%2A+2+%2A+-84+%29%29%2F%282%2A2%29+\"
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\n" ); document.write( "\"x+=+%28-11+%2B-+sqrt%28+121+-+%28-672%29+%29%29%2F%284%29+\"
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\n" ); document.write( "\"x+=+%28-11+%2B-+sqrt%28+121+%2B+672+%29%29%2F%284%29+\";minus a minus is a plus
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\n" ); document.write( "\"x+=+%28-11+%2B-+sqrt%28+793+%29%29%2F%284%29+\"
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\n" ); document.write( "\"x+=+%28-11+%2B+28.16%29%2F%284%29+\"; we only want the positive solution here
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\n" ); document.write( "\"x+=+%2B17.16%2F4\"
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\n" ); document.write( "x = 4.29 inches
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\n" ); document.write( "Find the dimension of the picture:
\n" ); document.write( "Length: 2(4.29) - 1 = 7.58 inches
\n" ); document.write( "Width = 4.29 inches
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\n" ); document.write( "Check our solution by finding the frame area:
\n" ); document.write( "(7.58+4) * (4.29+4) =
\n" ); document.write( " 11.58 * 8.29 = 95.998 ~ 96 sq/in, the given area
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\n" ); document.write( "Did this make sense to you? Any questions?
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