SOLUTION: When the side of a square is increased by four units, its area is increased by 80 square units. What is the length of the side of original square?

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Question 825541: When the side of a square is increased by four units, its area is increased by 80 square units. What is the length of the side of original square?
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the length of a side of the original square.
Then the original area is: x%5E2
And the length of the side of the expanded square would be: x+4
Then the area of the expanded square would be: %28x%2B4%29%5E2

With one variable we only need one equation to solve the problem. "When the side of a square is increased by four units, its area is increased by 80 square units." can be reworded as "the area of the expanded square is 80 square units more than the area of the original square." This reworded is probably easier to translate into:
%28x%2B4%29%5E2+=+x%5E2+%2B+80
Now we solve. First we simplify:
x%5E2%2B8x%2B16+=+x%5E2+%2B+80
Subtracting x%5E2 from each side:
8x%2B16+=+80
Subtracting 16 from each side:
8x+=+64
Dividing both sides by 8:
x+=+8
Since x is the length of the side of the original square and since that is what the problem asks for, we are finished.