SOLUTION: If the sides of a square are decreased by 3 cm, the area is decreased by 81 cm^2. What were the dimensions of the original square?

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Question 64411: If the sides of a square are decreased by 3 cm, the area is decreased by 81 cm^2. What were the dimensions of the original square?
Answer by funmath(2933) About Me  (Show Source):
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If the sides of a square are decreased by 3 cm, the area is decreased by 81 cm^2. What were the dimensions of the original square?
Let the original side be: x
Then the area is:x^2
Then if we decreased it by 3 the new sides would be: x-3
The area of the original decreased by 81 is: x^2-81
The area of the new square is:(x-3)^2
%28x-3%29%5E2=x%5E2-81
x%5E2-6x%2B9=x%5E2-81
x%5E2-x%5E2-6x%2B9=x%5E2-x%5E2-81
-6x%2B9=-81
-6x%2B9-9=-81-9
-6x=-90
-6x%2F-6=-90%2F-6
x=15
The original sides were 15 cm.
Sanity Check:
If the original sides were 15 cm, the area would be 15^2=225.
If the new sides were 15-3=12 cm, the area would be 12^2=144
If we subtract the two areas we get: 225-144=81
Happy Calculating!!!