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

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Question 83589: Help please.
If the sides of a square are decreased by 2cm, the area is decreased by 36cm^2. What were the dimensions of the original square?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the original dimension (side) of the square.
The original area would then be: A+=+x%5E2
Now if you decrease the original side by 2cm, you will have (x-2) and the new area can be found by %28x-2%29%5E2, which is given in the problem as x%5E2-36.
Now you can set up the equation to solve for x:
%28x-2%29%5E2+=+x%5E2-36 Simplify and solve for x.
x%5E2-4x%2B4+=+x%5E2-36 Subtract x%5E2from both sides.
-4x%2B4+=+-36Subtract 4 from both sides.
-4x+=+-40 Divide both sides by -4.
x+=+10 The dimensions of the original square were 10cm by 10cm.
Check:
The original area was:
A%5B0%5D+=+%2810%29%2810%29
A%5B0%5D+=+100 sq.cm.
The new area is:
A%5B1%5D+=+%2810-2%29%2A%2810-2%29
A%5B1%5D+=+8+X+8
A%5B1%5D+=+64sq.cm.
A%5B0%5D-A%5B1%5D+=+100-64 = 36sq.cm.