SOLUTION: If the sides of a square are decreased by 2 cm, the area is decreased by 36 cm2. What were the dimensions of the original square? Please help. I don't even know how to start.

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Question 414362: If the sides of a square are decreased by 2 cm, the area is decreased by
36 cm2. What were the dimensions of the original square?

Please help. I don't even know how to start.
Found 2 solutions by Earlsdon, MathLover1:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the length of the side of the original square and A its area, so...
A+=+x%5E2 Now decrease the sides by 2 cm (x-2). and the area by 36 (A-36), so now you have:
A-36+=+%28x-2%29%5E2 Substitute A+=+x%5E2
x%5E2-36+=+%28x-2%29%5E2 Simplify.
x%5E2-36+=+x%5E2-4x%2B4 Combine like-terms.
x%5E2-x%5E2+-36+=+-4x%2B4
-36+=+-4x%2B4 Add 36 to both sides.
0+=+-4x%2B40 Add 4x to both sides.
4x+=+40 Divide both sides by 4.
x+=+10
The dimensions of the original square were 10 by 10.
Check:
Original area:
A+=+10%5E2
A++100
New area:
%2810-2%29%5E2+=+64
Difference in the old and new areas:
100-64+=+36
The new area decreased by 36 sq.cm.

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

the sides of a square are all equal...let them be a
the area of a square is A=4a

If the sides of a square are decreased by 2 cm, we can write it as a-2cm

the area is decreased by 36+cm2, we can write it as A-36+cm2=a%5E2-36+cm2

What were the dimensions of the original square?
put these changes in original formula A=4a

%28a-2%29%5E2=a%5E2-36
a%5E2-4a%2B4=a%5E2-36
-4a=-36-4
-4a=-40
a=-40%2F-4
a=10+cm...the dimensions of the original square

check:
%2810-2%29%5E2=10%5E2-36
8%5E2=100-36
64=64