SOLUTION: If the sides of a sqare are decreased by 2 cm, the area is decreased by 36cm^2. What were teh dimensions of the original Square? This comes from a chapter on factoring and I for

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Question 77286: If the sides of a sqare are decreased by 2 cm, the area is decreased by 36cm^2. What were teh dimensions of the original Square? This comes from a chapter on factoring and I for the life of me can't see the formula correctly. I have been working out the problem as
36^2=x^2+x^2-2 but I know this is wrong?? Please HELP
Debbie
Found 2 solutions by Earlsdon, jim_thompson5910:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let the side of the origimal square be of length x.
The original area is then x%5E2 After decreasing the original side length by 2 (x-2), the new area is decreased by 36 sq.cm.(x%5E2-36).
So, you can write:
%28x-2%29%5E2+=+x%5E2-36 Simplify and solve for x.
x%5E2-4x%2B4+=+x%5E2-36 Subtract x%5E2 from both sides.
-4x%2B4+=+-36 Subtract 4 from both sides.
-4x+=+-40 Divide both sides by -4.
x+=+10
The length of the side of the original square is 10 cm.
Check:
Original area is 10X10 = 100 sq.cm.
The new area is (10-2)X(10-2) = 8X8 = 64 sq.cm
The difference: 100-64 = 36 sq.cm.

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If we have an original square of side x we have the area as:
x%2Ax=x%5E2
So if we decrease the sides by 2 and it results in a decrease of 36 cm%5E2 we get
%28x-2%29%28x-2%29=x%5E2-36
x%5E2-4x%2B4=x%5E2-36 foil the left side
-4x%2B2=-36 Subtract x%5E2 from both sides
-4x=-40 Subtract 2 from both sides
x=-40%2F%28-4%29 Divide both sides by -4
So the original side is
x=10


Check:
%2810-2%29%2810-2%29=%2810%29%5E2-36 Plug in x=10
%288%29%288%29=100-36
64=64 works