rxs0005 wrote:

Is the perimeter of the equilateral triangle T greater than the perimeter of the square S

The ratio of the area of T to area of S is root (3) : 1

The ratio of length of a side of T to a side of T is 2 : 1

\(P_{equilateral}=3t\) and \(P_{square}=4s\), where \(t\) and \(s\) are the sides of triangle and square respectively. Question: is \(P_{equilateral}>P_{square}\). You can notice that if we knew the ratio of the side \(t\) to the side \(s\) then we would be able to answer the question.

(1) The ratio of the area of T to area of S is root (3) : 1 --> both the area of the equilateral triangle (\(area_{equilateral}=t^2\frac{\sqrt{3}}{4}\)) and the area of a square (\(area_{square}=s^2\)) can be expressed with their sides, so we could get the ratio of the sides from the ratio of the areas. Sufficient.

(2) The ratio of length of a side of T to a side of

S is 2 : 1 --> directly gives us the ratio of the sides. Sufficient.

Answer: D.

What I'm unclear about is the formula t squared=root 3 divided by four. Does that formula give the ratio of the sides? Like if the sides of an equilateral were 2 : 2 : 2 then would 2^2 times root divided by four equal the ratio of the side of a square- does that mean the side of a square is 2 root 3 then? Two squared= 4 times root 3 divided by four then cancels out to root 3 then multiply 2 by root 3 and that's the length of the side of the square?