SOLUTION: In order to triple the area of a square, the new side lengths must be equal to the old side lengths multiplied by: F) Square root of 3. G) 3 H) 9 J) Square root of 27. K)27

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Question 1083068: In order to triple the area of a square, the new side lengths must be equal to the old side lengths multiplied by:
F) Square root of 3.
G) 3
H) 9
J) Square root of 27.
K)27
I selected "9", but the answer is "F", the square root of 3.
This is an SAT practice question. I am trying to figure how the answer is F.
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


First, let's begin with the reason the answer is most assuredly not 9.

The area of a square is given by the square of the measure of one side, that is:



So if you made the side of the new square 9 times the side of the old square, the new area would be:



81 times more area than the original

But if we want the area to only be 3 times the original area, that is



To find the measure of the side that would give this result, we take the square root of the area:



John

My calculator said it, I believe it, that settles it