Question 472266: If you double the length of the side of a square, what is the ratio of the areas of the square?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! should be 4.
the formula for the area of a square is:
s^2 = A
if you double the length of each side, then the equation becomes:
(2s)^2 = A which becomes
4s^2 = A
if you triple the length of each side, then the equation becomes:
(3s)^2 = A which becomes:
9s^2 = A
the ratio of the increase in the length of a side to the increase in the area of the square would be x^2 which means that if the length of a side is increased by a multiplication factor of x, then the area is increased by a multiplication factor of x^2.
this works with multiplication.
it does not work with addition.
if the side of a square is s and you increase the length of the side by adding x to it, then the increase in the area would be given by the equation of:
(s+x)^2 = A
this is not the same as (s*x)^2
(s*x)^2 is equivalent to s^2*x^2
(s+x)^2 is equivalent to s^2 + 2xs + x^2
it's a different relationship.
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