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If the sides of a square are decreased by 3cm, the area is decreased by 81cm^2.What were the dimensions of the original square?
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\n" ); document.write( "Let 1 side of the original square = x
\n" ); document.write( "Then the area of the original square = x^2
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\n" ); document.write( "The side of the smaller square would = (x-2); original side decreased by 2cm
\n" ); document.write( "Area of the small square = (x-2)^2
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\n" ); document.write( "Problem states:
\n" ); document.write( "Original square area - smaller square area = 81 sq/cm
\n" ); document.write( " x^2 - (x-2)^2 = 81
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\n" ); document.write( "FOIL (x-2)(x-2)
\n" ); document.write( "x^2 -(x^2 - 4x + 4) = 81
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\n" ); document.write( "Remove brackets, remember to change the signs inside the brackets:
\n" ); document.write( "x^2 - x^2 + 4x - 4 = 81
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\n" ); document.write( "conveniently, the x^2's are eliminated:
\n" ); document.write( "4x = 81 + 4
\n" ); document.write( "4x = 85
\n" ); document.write( "x = 85/4
\n" ); document.write( "x = 21.25 cm is the side of the original square:
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\n" ); document.write( "The smaller square would be 21.25 - 2 = 19.25
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\n" ); document.write( "Check our solution by finding the area of each square:
\n" ); document.write( "21.25^2 = 451.5625
\n" ); document.write( "19.25^2 = 370.5625
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\n" ); document.write( "Differ by 81.00 sq/cm as given
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\n" ); document.write( "Could you follow this OK? Any questions?
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