SOLUTION: How many times the sides of a square would increase if the area was increased by nine times?

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Question 498614: How many times the sides of a square would increase if the area was increased by nine times?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let the length of the side of the square be s.
The area of the square is given by:
A+=+s%5E2 Increase the area by 9 means: 9A and we'll show the increase in the length of the side by: n%2As, so...
9A+=+%28n%2As%29%5E2 but A+=+s%5E2 so we substitute...
9%28s%5E2%29+=+%28n%2As%29%5E2 Simplify and solve for s.
9s%5E2+=+n%5E2%2As%5E2 Divide both sides by s%5E2
9+=+n%5E2 Take the square root.
3+=+n
So the sides of the square (s) would increase by 3 times.