SOLUTION: c...
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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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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You can put this solution on YOUR website! 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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Let 1 side of the original square = x
Then the area of the original square = x^2
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The side of the smaller square would = (x-2); original side decreased by 2cm
Area of the small square = (x-2)^2
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Problem states:
Original square area - smaller square area = 81 sq/cm
x^2 - (x-2)^2 = 81
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FOIL (x-2)(x-2)
x^2 -(x^2 - 4x + 4) = 81
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Remove brackets, remember to change the signs inside the brackets:
x^2 - x^2 + 4x - 4 = 81
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conveniently, the x^2's are eliminated:
4x = 81 + 4
4x = 85
x = 85/4
x = 21.25 cm is the side of the original square:
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The smaller square would be 21.25 - 2 = 19.25
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Check our solution by finding the area of each square:
21.25^2 = 451.5625
19.25^2 = 370.5625
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Differ by 81.00 sq/cm as given
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Could you follow this OK? Any questions?
