SOLUTION: If the sides of a square are decreased by 2cm, the area is decreased by 36 cm squared. What were the dimensions of the original square?

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Start with defining a variable to represent the length of a side of the original square, let's call it x.
So the area of the original square would be .

The new square is 2 cm shorter on each side, so one of the sides must measure , and the area of the new square must be .

But we know that . Substituting: .

Now, expand the binomial, collect terms, and put the equation in standard form.







So the original square was 10 cm on a side.

Let's check the answer.

Original area
New area
, Check.