document.write( "Question 901799: by decreasing each dimension by 2 units, the area of a rectangle decrease from 40 square feet (on left) to 16 square feet (on the right). find the percent decrease in area \n" ); document.write( "
Algebra.Com's Answer #546989 by stanbon(75887)\"\" \"About 
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by decreasing each dimension by 2 units, the area of a rectangle decrease from 40 square feet (on left) to 16 square feet (on the right). find the percent decrease in area
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\n" ); document.write( "Draw a rectangle inside a rectangle.
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\n" ); document.write( "Dimensions of the outer area are x and y
\n" ); document.write( "Area = x*y = 40 sq. ft.
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\n" ); document.write( "Dimensions of the inner rectangle are (x-2) and (y-2)
\n" ); document.write( "Area = (x-2)(y-2)
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\n" ); document.write( "Equations::
\n" ); document.write( "xy = 40 sq ft
\n" ); document.write( "(x-2)(y-2) = 16 sq ft
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\n" ); document.write( "xy -2x -2y + 4 = 16
\n" ); document.write( "Substitute for \"xy\" to get:
\n" ); document.write( "40 -2x -2y = 12
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\n" ); document.write( "2x + 2y = 28
\n" ); document.write( "x + y = 14
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\n" ); document.write( "Using x+y = 14 , substitute for \"y\" and solve for \"x\"::
\n" ); document.write( "xy = 40
\n" ); document.write( "x(14-x) = 40
\n" ); document.write( "14x - x^2 = 40
\n" ); document.write( "x^2 - 14x + 40 = 0
\n" ); document.write( "Factor::
\n" ); document.write( "(x-10)(x-4) = 0
\n" ); document.write( "If x = 10, y = 4
\n" ); document.write( "If x = 4, y = 10
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\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.\r
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