SOLUTION: If the sides of a square are decreased by 3 cm, the area is decreased by 81cm^2. What were the dimensions of the original square? Could someone please help me, this has thrown me o

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Question 120535: If the sides of a square are decreased by 3 cm, the area is decreased by 81cm^2. What were the dimensions of the original square? Could someone please help me, this has thrown me off! Thank you so much in advance.
Found 2 solutions by solver91311, josmiceli:
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!
Let s be the side of the original square. Then the area of the original square would be A%5Bo%5D=s%5E2. If you decrease the sides by 3 cm, then the side of the new square would be s-3, and the area of the new square would be A%5Bn%5D=%28s-3%29%5E2. But we know that the new square has 81cm%5E2 less area than the old square, so we can write:

A%5Bo%5D=A%5Bn%5D%2B81

Substituting:

s%5E2=%28s-3%29%5E2%2B81

Now, expand the binomial, collect like terms, and solve the result

s%5E2=s%5E2-6s%2B9%2B81
s%5E2=s%5E2-6s%2B90

Add -s%5E2%2B6s to both sides

6s=90

Divide by 6

s=15

Check the answer:
15%5E2=225 and %2815-3%29%5E2=12%5E2=144. 225-144=81, answer checks.

Hope that helps,
John

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Call the sides of the original square x
The area of the original square is x%5E2
When I decrease the sides by 3 cm, I have an area
of %28x+-+3%29%28x+-+3%29
In words:
81 cm^2 = (original area) - (area reduced by 3cm on each side)
81+=+x%5E2+-+%28x+-+3%29%5E2
81+=+x%5E2+-+%28x%5E2+-+6x+%2B+9%29
6x+-+9+=+81
6x+=+90
x+=+15
The original square is 15 cm x 15 cm