SOLUTION: Geometry. If the sides of a square are decreased by 2cmm the area is decreased by 36cm^2. What were the dimensions of the original square?: I did not see how this was solved???

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Question 72608: Geometry. If the sides of a square are decreased by 2cmm the area is decreased by 36cm^2. What were the dimensions of the original square?:
I did not see how this was solved???
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
Let the original length of the side of the square be represented by L. Since the area of a
square equals the square of a side we can by letting A represent the original area write the
equation:
.
A+=+L%5E2
.
Now what happens when we decrease the length of the side by 2 cm? The new length of the side
is the old length minus 2 cm or L - 2. And we are told that the new area of the square is
old area A minus 36 square cm or A - 36. Now for the new square, let's write the area equation
that says the Area = the square of a side:
.
A+-+36+=+%28L-2%29%5E2
.
but we said previously that A is equal to L%5E2. Substituting L%5E2 for A into our
equation we get:
.
L%5E2+-+36+=+%28L-2%29%5E2
.
and by squaring the right side we get:
.
L%5E2+-+36+=+L%5E2+-+4L+%2B+4
.
Then you can subtract L^2 from both sides to reduce the equation to:
.
-36+=+-4L+%2B+4
.
Add 4L to both sides to get:
.
4L+-+36+=+4
.
Then add 36 to both sides:
.
4L+=+40
.
Finally, divide both sides by 4 to end up with L+=+10 and the answer is in cm. So the
dimensions of the original square (represented by L) were 10 cm on a side.
.
Hope this untangles the problem for you and helps you to see how to deal with problems such
as these.