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If the sides of a square are increased by 3 cm, the area is decreased by 36 cm^2. What were the dimensions of the original square? Please show me the formula and how to work.

That doesn't sound possible.

If the sides of a square are increased, the area must also be increased.

Ms.Sue is correct. You may have copied down the problem incorrectly.

If increasing the sides by three INCREASES the area by 36, and the orginal side length is a, then
(a+3)^2 = a^2 + 36
a^2 + 6x + 9 = a^2 + 36
Subtract out the a^2 terms on both sides.
6x = 27
x = 4.5

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