Question 72608
Let the original length of the side of the square be represented by L. Since the area of a 
square equals the square of a side we can by letting A represent the original area write the
equation:
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{{{A = L^2}}}
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Now what happens when we decrease the length of the side by 2 cm? The new length of the side
is the old length minus 2 cm or L - 2.  And we are told that the new area of the square is
old area A minus 36 square cm or A - 36.  Now for the new square, let's write the area equation
that says the Area = the square of a side:
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{{{A - 36 = (L-2)^2}}}
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but we said previously that A is equal to {{{L^2}}}. Substituting {{{L^2}}} for A into our
equation we get:
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{{{L^2 - 36 = (L-2)^2}}}
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and by squaring the right side we get:
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{{{L^2 - 36 = L^2 - 4L + 4}}}
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Then you can subtract L^2 from both sides to reduce the equation to:
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{{{-36 = -4L + 4}}}
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Add 4L to both sides to get:
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{{{4L - 36 = 4}}}
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Then add 36 to both sides:
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{{{4L = 40}}}
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Finally, divide both sides by 4 to end up with {{{L = 10}}} and the answer is in cm. So the 
dimensions of the original square (represented by L) were 10 cm on a side.
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Hope this untangles the problem for you and helps you to see how to deal with problems such 
as these.