SOLUTION: If the sides of a square are decreased by 3cm, the area is decreased by 81cm squared. What were the dimensions of the original square? I was also wondering if you could show the wo

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Question 52282: If the sides of a square are decreased by 3cm, the area is decreased by 81cm squared. What were the dimensions of the original square? I was also wondering if you could show the work you used to get to the solution, thank you.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let the original side of the square be s.
The area of the original square is: A+=+s%5E2
If you decrease s by 3 you'll have s-3.
The area of the new square will be:
a+=+%28s-3%29%5E2
a+=+s%5E2-6s%2B8 and this is equal to the original area s%5E2 decreased by 81. Putting this all together, we get:
s%5E2-6s%2B9+=+s%5E2-81 Simplify and solve for s, the length of the side of the original square. Subtract s%5E2 from both sides.
-6s%2B9+=+-81 Subtract 9 from both sides.
-6s+=+-90 Divide both sides by -6.
s+=+15
The dimensions of the original square were:
15 cm. by 15 cm.